imaging & therapeutic technology three ......783 imaging & therapeutic technology...

783

IMAGING & THERAPEUTIC TECHNOLOGY

Abbreviations: MIP = maximum intensity projection, PD = proton density, PET = positron emission tomography, 3D =three-dimensional, 2D = two-dimensional

Index terms: Computed tomography (CT) • Computers • Computers, simulation • Images, analysis • Images, displayImages, processing • Magnetic resonance (MR) • Single-photon emission tomography (SPECT) • Ultrasound (US)

RadioGraphics 1999; 19:783–806

1From the Department of Radiology, University of Pennsylvania, 423 Guardian Dr, Philadelphia, PA 19104-6021. ReceivedApril 21, 1998; revision requested May 21 and received December 14; accepted December 21. Address reprint requeststo the author.

©RSNA, 1999

Three-dimensionalVisualization andAnalysis Methodologies:A Current Perspective1

Jayaram K. Udupa, PhD

Three-dimensional (3D) imaging was developed to provide both qualitative andquantitative information about an object or object system from images obtainedwith multiple modalities including digital radiography, computed tomography,magnetic resonance imaging, positron emission tomography, single photonemission computed tomography, and ultrasonography. Three-dimensional im-aging operations may be classified under four basic headings: preprocessing,visualization, manipulation, and analysis. Preprocessing operations (volume ofinterest, filtering, interpolation, registration, segmentation) are aimed at ex-tracting or improving the extraction of object information in given images. Vi-sualization operations facilitate seeing and comprehending objects in their fulldimensionality and may be either scene-based or object-based. Manipulationmay be either rigid or deformable and allows alteration of object structures andof relationships between objects. Analysis operations, like visualization opera-tions, may be either scene-based or object-based and deal with methods ofquantifying object information. There are many challenges involving matters ofprecision, accuracy, and efficiency in 3D imaging. Nevertheless, 3D imaging isan exciting technology that promises to offer an expanding number and vari-ety of applications.

■■■■■ INTRODUCTIONThe main purpose of three-dimensional (3D) imaging is to provide both qualitativeand quantitative information about an object or object system from images obtainedwith multiple modalities including digital radiography, computed tomography (CT), mag-netic resonance (MR) imaging, positron emission tomography (PET), single photonemission computed tomography (SPECT), and ultrasonography (US). Objects that arestudied may be rigid (eg, bones), deformable (eg, muscles), static (eg, skull), dynamic(eg, heart, joints), or conceptual (eg, activity regions in PET, SPECT, and functional MRimaging; isodose surfaces in radiation therapy).

At present, it is possible to acquire medical images in two, three, four, or even fivedimensions. For example, two-dimensional (2D) images might include a digital radio-graph or a tomographic section obtained with CT, MR imaging, PET, SPECT, or US; a3D image might be used to demonstrate a volume of tomographic sections of a staticobject; a time sequence of 3D images of a dynamic object would be displayed in four

784 ■■■■■ Imaging & Therapeutic Technology Volume 19 Number 3

dimensions; and an image of a dynamic objectfor a range of parameters (eg, MR spectro-scopic images of a dynamic object) would bedisplayed in five dimensions.

It is not currently feasible to acquire truly re-alistic-looking four- and five-dimensional im-ages; consequently, approximations are made.In most applications, the object system beinginvestigated consists of only a few static ob-jects. For example, a 3D MR imaging study ofthe head may focus on white matter, gray mat-ter, and cerebrospinal fluid.

A textbook with a systematic presentation of3D imaging is not currently available. However,edited works may be helpful for readers unfa-miliar with the subject (1–3). The reference listat the end of this article is representative butnot exhaustive.

In this article, we provide an overview ofthe current status of the science of 3D imaging,identify the primary challenges now being en-countered, and point out the opportunitiesavailable for advancing the science. We de-scribe and illustrate the main 3D imaging op-erations currently being used. In addition, wedelineate major concepts and attempt to clearup some common misconceptions. Our in-tended audience includes developers of 3D im-aging methods and software as well as develop-ers of 3D imaging applications and cliniciansinterested in these applications. We assumethe reader has some familiarity with medicalimaging modalities and a knowledge of the ru-dimentary concepts related to digital images.

■■■■■ CLASSIFICATION OF 3D IMAGINGOPERATIONSThree-dimensional imaging operations can bebroadly classified into the following categories:(a) preprocessing (defining the object systemto create a geometric model of the objects un-der investigation), (b) visualization (viewing andcomprehending the object system), (c) manipu-lation (altering the objects [eg, virtual surgery]),and (d) analysis (quantifying information aboutobject system). These operations are highly in-

terdependent. For example, some form of visu-alization is essential to facilitate the other threeclasses of operations. Similarly, object defini-tion through an appropriate set of preprocess-ing operations is vital to the effective visualiza-tion, manipulation, and analysis of the objectsystem. We use the phrase “3D imaging” to col-lectively refer to these four classes of operations.

A monoscopic or stereoscopic video displaymonitor of a computer workstation is the mostcommonly used viewing medium for images.However, other media such as holographyand head-mounted displays are also available.Unlike the 2D computer monitor, holographyoffers a 3D medium for viewing. The head-mounted display basically consists of two tinymonitors positioned in front of the eyes as partof a helmetlike device worn by the user. Thisarrangement creates the sensation of being freefrom one’s natural surroundings and immersedin an artificial environment. However, the com-puter monitor is by far the most commonlyused viewing medium, mainly because of itssuperior flexibility, speed of interaction, andresolution compared with other media.

A generic 3D imaging system is representedin Figure 1. A workstation with appropriatesoftware implementing 3D imaging operationsforms the core of the system. A wide variety ofinput or output devices are used depending onthe application. On the basis of the core of thesystem (ie, independent of input or output), 3Dimaging systems may be categorized as thosehaving (a) physician display consoles providedby imaging equipment vendors, (b) image pro-cessing and visualization workstations suppliedby other independent vendors, (c) 3D imagingsoftware supplied independent of the worksta-tion, and (d) university-based 3D imaging soft-ware (often freely available via the Internet).

Systems produced by scanner manufacturersand workstation vendors usually provide effec-tive solutions but may cost $50,000–$150,000.For users with expertise in accessing, install-ing, and running the software, university-based3D imaging software is available that can pro-vide very effective, inexpensive solutions. For

Figure 1. Schematic illustratesa typical 3D imaging system.

May-June 1999 Udupa ■■■■■ RadioGraphics ■■■■■ 785

example, for under $5,000 it is possible to con-figure a complete system running on modernpersonal computers (eg, Pentium 300; Intel, SantaClara, Calif) that performs as well as or evenbetter than the costly systems described in theother three categories.

●●●●● TerminologySome frequently used terms in 3D imaging aredefined in the Table and illustrated in Figure 2.

The region of the image corresponding tothe anatomic region of interest is divided intorectangular elements (Fig 2). These elementsare usually referred to as pixels for 2D imagesand voxels for 3D images; in this article, how-ever, we refer to them as voxels for all images.In 2D imaging, the voxels are usually squares,whereas in 3D imaging they are cuboids with asquare cross section.

●●●●● Object Characteristics in ImagesThere are two important object characteristicswhose careful management is vital in all 3D im-

aging operations: graded composition and “hang-ing-togetherness.”

Graded Composition.—Most objects in thebody have a heterogeneous material composi-tion. In addition, imaging devices introduceblurring into acquired images due to variouslimitations. As a result, regions correspondingto the same object display a gradation of sceneintensities. On the knee CT scan shown in Fig-ure 3, both the patella and the femur exhibitthis property (ie, the region corresponding tobone in these anatomic locations has not justone CT value but a gradation of values).

Hanging-togetherness (Gestalt).—Despitethe gradation described in the preceding para-graph, when one views an image, voxels seemto “hang together” (form a gestalt) to form anobject. For example, the high-intensity voxelsof the patella do not (and should not) hang to-gether with similar voxels in the femur, althoughvoxels with dissimilar intensities in the femurhang together (Fig 3).

Frequently Used Terms in 3D Imaging

Term Definition

Scene Multidimensional image;rectangular array ofvoxels with assignedvalues

Scene domain Anatomic region repre-sented by the scene

Scene intensity Values assigned to thevoxels in a scene

Pixel size Length of a side of thesquare cross section ofa voxel

Scanner coordinate Origin and orthogonal axessystem system affixed to the

imaging deviceScene coordinate Origin and orthogonal axes

system system affixed to thescene (origin usuallyassumed to be upperleft corner of first sectionof scene, axes are edgesof scene domain thatconverge at the origin)

Object coordinate Origin and orthogonal axessystem system affixed to the ob-

ject or object systemDisplay coordinate Origin and orthogonal

system axes system affixed tothe display device

Rendition 2D image depicting theobject information cap-tured in a scene or objectsystem

Figure 2. Drawing provides graphic representationof the basic terminology used in 3D imaging. abc =scanner coordinate system, rst = display coordinatesystem, uvw = object coordinate system, xyz = scenecoordinate system.


■■■■■ PREPROCESSINGThe aim of preprocessing operations is to takea set of scenes and output computer object mod-els or another set of scenes from the given set,which facilitates the creation of computer ob-ject models. The most commonly used opera-tions are volume of interest, filtering, interpola-tion, registration, and segmentation.

●●●●● Volume of InterestVolume of interest converts a given scene intoanother scene. Its purpose is to reduce theamount of data by specifying a region of inter-est and a range of intensity of interest.

A region of interest is specified by creating arectangular box that delimits the scene domainin all dimensions (Fig 4a). A range of intensityof interest is specified by designating an inten-sity interval. Within this interval, scene intensi-ties are transferred unaltered to the output. Out-side the interval, they are set to the lower andupper limits. The range of intensity of interestis indicated as an interval on a histogram of thescene (Fig 4b). The corresponding section inthe output scene is shown in Figure 4c. Thisoperation can often reduce storage require-ments for scenes by a factor of 2–5. It is advis-able to use the volume of interest operationfirst in any sequence of 3D imaging operations.

The challenge in making use of the volumeof interest operation is to completely automatethis operation and to do so in an optimal fash-ion, which requires explicit delineation of ob-jects at the outset.

●●●●● FilteringFiltering converts a given scene into anotherscene. Its purpose is to enhance wanted (object)information and suppress unwanted (noise,background, other object) information in theoutput scene. Two kinds of filters are available:suppressing filters and enhancing filters. Ide-ally, unwanted information is suppressed with-out affecting wanted information and wantedinformation is enhanced without affecting un-wanted information.

The most commonly used suppressing filteris a smoothing operation used mainly for sup-pressing noise (Fig 5a, 5b). In this operation, avoxel v in the output scene is assigned an in-tensity that represents a weighted average ofthe intensities of voxels in the neighborhood ofv in the input scene (4). Methods differ as tohow neighborhoods are determined and howweight is assigned (5). Another commonly usedmethod is median filtering. In this method,the voxel v in the output scene is assigned avalue that simply represents the middle value

(median) of the intensities of the voxels in theneighborhood of v in the input scene when thevoxels are arranged in ascending order.

In another method (5), often used in process-ing MR images, a process of diffusion and flowis considered to govern the nature and extentof smoothing. The idea is that in regions ofvoxels with a low rate of change in intensity,voxel intensities diffuse and flow into neigh-boring regions. This process is prevented byvoxels with a high rate of change in intensity.Certain parameters control the extent of diffu-sion that takes place and the limits of the mag-nitude of the rate of change in scene intensitythat are considered “low” and “high.” Thismethod is quite effective in overcoming noisebut sensitive enough not to suppress subtle de-tails or blur edges.

The most commonly used enhancing filter isan edge enhancer (Fig 5c) (4). With this filter,the intensity of a voxel v in the output is therate of change in the intensity of v in the input.If we think of the input scene as a function,then this rate of change is given by the magni-tude of the gradient of the function. Becausethis function is not known in analytic form,various digital approximations are used for thisoperation. The gradient has a magnitude (rate ofchange) and a direction in which this change ismaximal. For filtering, the direction is usually

Figure 3. Graded composition and hanging-to-getherness. CT scan of the knee illustrates gradedcomposition of intensities and hanging-togetherness.Voxels within the same object (eg, the femur) areassigned considerably different values. Despite thisgradation of values, however, it is not difficult toidentify the voxels as belonging to the same object(hanging-togetherness).


a. b.

Figure 4. Preprocessing with a volume of inter-est operation. (a) Head CT scan includes a speci-fied region of interest (rectangle). (b) Histogramdepicts the intensities of the scene designated ina and includes a specified intensity of interest.(c) Resulting image corresponds to the specifiedregion of interest in a.

c.

a. b. c.

Figure 5. Preprocessing with suppressing and enhancing filters. (a) Head CT scan illustrates the appearanceof an image prior to filtering. (b) Same image as in a after application of a smoothing filter. Note that noise issuppressed in regions of uniform intensity, but edges are also blurred. (c) Same image as in a after applicationof an edge-enhancing filter. Note that regions of uniform intensity are unenhanced because the gradient in theseregions is small. However, the boundaries (especially of skin and bone) are enhanced.


ignored, although it is used in operations usedto create renditions. Methods differ as to howto determine the digital approximation, whichis extensively studied in computer vision (6).

Unfortunately, most existing suppressing fil-ters often also suppress object information andenhancing filters enhance unwanted informa-tion. Explicit incorporation of object knowledgeinto these operations is necessary to minimizethese effects.

●●●●● InterpolationLike filtering, interpolation converts a givenscene into another scene. Its purpose is tochange the level of discretization (sampling)of the input scene. Interpolation becomes nec-essary when the objective is (a) to change thenonisotropic discretization of the input sceneto isotropic discretization or to a desired levelof discretization, (b) to represent longitudinalscene acquisitions in a registered common co-ordinate system, (c) to represent multimodalityscene acquisitions in a registered coordinatesystem, or (d) to re-section the given scene.Two types of interpolation are currently avail-able: scene-based interpolation and object-basedinterpolation.

Scene-based Interpolation.—The intensityof a voxel v in the output scene is determinedon the basis of the intensity of voxels in theneighborhood of v in the input scene. Methodsdiffer as to how the neighborhoods are deter-mined and what form of the functions of theneighboring intensities is used to estimate the

intensity of v (3,6,7). In 3D interpolation, thesimplest solution is to estimate new sectionsbetween sections of the input scene, keepingthe pixel size of the output scene the same asthat of the input scene. This leads to a one-di-mensional interpolation problem: estimatingthe scene intensity of any voxel v in the outputscene from the intensities of voxels in the in-put scene on the two sides of v in the z direc-tion (the direction orthogonal to the sections).In “nearest neighbor” interpolation, v is as-signed the value of the voxel that is closest to vin the input scene. In linear interpolation, twovoxels v

1 and v

2 (one on either side of v) are

considered. The value of v is determined withthe assumption that the input scene intensitychanges linearly from the intensity at v

1 to that

at v2. In higher-order (eg, cubic) interpolations,

more neighboring voxels are considered.When the size of v in the output scene differsin all dimensions from that of voxels in the in-put scene, the situation becomes more general,and intensities are assumed to vary linearly oras a higher-order polynomial in each of thethree directions in the input scene.

Object-based Interpolation.—Object infor-mation derived from scenes is used to guidethe interpolation process. At one extreme (8),the given scene is first converted to a “binary”scene (ie, a scene with only two intensities:0 and 1) with a segmentation operation (see“Segmentation”). The voxels with a value of 1represent the object of interest, whereas thevoxels with a value of 0 represent the rest ofthe scene domain. The “shape” of the region

a. b.

Figure 6. Shape-based interpolation of a binary CT scene created by designating a threshold.(a) CT scene after shape-based interpolation at a “coarse” resolution and subsequent surfacerendering. (b) The same scene after interpolation at a “fine” resolution and surface rendering.


represented by the “1” voxels (the object) isthen used to create an output binary scene witha similar shape (9,10) by way of interpolation.This is done by first converting the binary sceneback into a (gray-valued) scene by assigning ev-ery voxel in this scene a value that representsthe shortest distance between the voxel andthe boundary between the “0” voxels and the “1”voxels. The “0” voxels are assigned a negativedistance, whereas the “1” voxels are assigned apositive distance. This scene is then interpolatedwith a scene-based technique and is subsequentlyconverted back to a binary scene by setting athreshold at 0. At the other extreme, the shapeof the intensity profile of the input scene is it-self considered an “object” to be used to guideinterpolation so that this shape is retained asfaithfully as possible in the output scene (11).For example, in the interpolation of a 2D scenewith this method, the scene is converted into a 3Dsurface of intensity profile wherein the heightof the surface represents pixel intensities. This(binary) object is then interpolated with a shape-based method. Several methods exist betweenthese two extremes (12,13). The shape-basedmethods have been shown to produce more ac-curate results (8–11) than most of the commonlyused scene-based methods.

Figure 6 demonstrates binary shape-based in-terpolation of an image derived from CT data atcoarse and fine levels of discretization. The origi-

nal 3D scene was first assigned a threshold tocreate a binary scene. This binary scene wasthen interpolated at coarse (Fig 6a) and fine(Fig 6b) levels and surface rendered.

The challenge in interpolation is to identifyspecific object information and incorporate itinto the process. With such information, theaccuracy of interpolation can be improved.

●●●●● RegistrationRegistration takes two scenes or objects as in-put and outputs a transformation that, whenapplied to the second scene or object, matchesit as closely as possible to the first. Its purposeis to combine scene or object information frommultiple modalities and protocols to determinechange, growth, motion, and displacement ofobjects as well as aid in object identification.Registration may be either scene-based or ob-ject-based.

Scene-based Registration.—To match twoscenes, a rigid transformation made with trans-lation and rotation (and often scaling) is calcu-lated for one scene S

2 such that the intensity

pattern of the transformed scene (S2′) matches

that of the first scene (S1) as closely as possible

(Fig 7) (14). Methods differ with respect to thematching criterion used and the means of

a.

b.

Figure 7. Scene-based registration. (a) Three-dimensional scenes corresponding to proton-density (PD)–weightedMR images of the head obtained in a patient with multiple sclerosis demonstrate a typical “preregistration” ap-pearance. The scenes were acquired at four different times. (b) Same scenes as in a after 3D registration. Theprogression of the disease (hyperintense lesions around the ventricles) is now readily apparent. At registration,the scenes were re-sectioned with a scene-based interpolation method to obtain sections at the same location.


determining which of the infinite number ofpossible translations and rotations are optimal(15). Scene-based registration methods are alsoavailable for cases in which objects undergoelastic (nonrigid) deformation (16).

Object-based Registration.—In object-basedregistration, two scenes are registered on thebasis of object information extracted from thescenes. Ideally, the two objects should be assimilar as possible. For example, to match 3Dscenes of the head obtained with MR imagingand PET, one may use the outer skin surface ofthe head as computed from each scene andmatch the two surfaces (17). Alternatively (orin addition), landmarks such as points, curves,or planes that are observable in and computablefrom both scenes as well as implanted objectsmay be used (18–20). Optimal translation androtation parameters for matching the two ob-jects are determined by minimizing some mea-sure of “distance” between the two (sets of)objects. Methods differ as to how distances aredefined and optimal solutions are computed.

Rigid object-based registration is illustratedin Figure 8. In contrast, deformable matchingoperations can also be used on objects (21,22).These operations may be more appropriate thanrigid matching for nonrigid soft-tissue structures.Typically, a global approximate rigid matchingoperation is performed, followed by local de-formations for more precise matching. Deform-able registration is also used to match comput-erized brain atlases to brain scene data obtainedin a given patient (23). Initially, some object in-formation has to be identified in the scene.This procedure has several potential applica-tions in functional imaging, neurology, and neu-rosurgery as well as in object definition per se.

The challenge in registration is that scene-based methods require that the intensity pat-terns in the two scenes be similar. This is oftennot the case, however. Converting scenes intofuzzy (nonbinary) object descriptions that re-

tain object gradation can potentially overcomethis but may still retain the strength of scene-based methods. Deformable fuzzy object match-ing seems natural and appropriate in most situ-ations but will require the development of fuzzymechanics theory and algorithms.

●●●●● SegmentationFrom a given set of scenes, segmentation out-puts computer models of object informationcaptured in the scenes. Its purpose is to iden-tify and delineate objects. Segmentation con-sists of two related tasks: recognition and delin-eation.

Recognition.—Recognition consists of roughlydetermining the whereabouts of an object inthe scene. In Figure 3, for example, recognitioninvolves determining that “this is the femurand this is the patella.” This task does not in-volve the precise specification of the regionoccupied by the object.

Recognition may be accomplished either au-tomatically or with human assistance. In auto-matic (knowledge- and atlas-based) recogni-tion, artificial intelligence methods are used torepresent knowledge about objects and theirrelationships (24–26). Preliminary delineationis usually needed in these methods to extractobject components and to form and test hy-potheses related to whole objects.

A carefully created “atlas” consisting of acomplete description of the geometry and in-terrelationships of objects is used (16,27,28).Some delineation of object components in thegiven scene is necessary. This information isused to determine the mapping necessary totransform voxels or other geometric elementsfrom the scene space to the atlas. Conversely,the information is also used to deform the atlasso that it matches the delineated object compo-nents in the scene.

In human-assisted recognition, simple assis-tance is often sufficient to help solve a segmen-tation problem. This assistance may take severalforms: for example, specification of several

Figure 8. Rigid object-basedregistration. Sequence of 3D MRimaging scenes of the foot al-lows kinematic analysis of themidtarsal joints. The motion (ie,translation and rotation) of thetalus, calcaneus, and navicularand cuboid bones from one po-sition to the other is determinedby registering the bone surfacesin the two different positions.


“seed” voxels inside the 3D region occupiedby the object or on its boundary, creation of abox (or some other simple geometric shape)that just encloses the object and can be quicklyspecified, or a click of a mouse button to ac-cept a real object (eg, a lesion) or reject a falseobject.

Delineation.—Delineation involves determin-ing the precise spatial extent and compositionof an object including gradation. In Figure 3, ifbone is the object system of interest, then de-lineation consists of defining the spatial extentof the femur and patella separately and specify-ing an “objectness” value for each voxel ineach object. Once the objects are defined sepa-rately, the femur and the patella can be visual-ized, manipulated, and analyzed individually.

Delineation may be accomplished with a va-riety of methods. Often, delineation is itselfconsidered to be the entire segmentation prob-lem, in which case related solutions are consid-ered to be solutions to the segmentation prob-lem. However, it is helpful to distinguish be-tween recognition and delineation to understandand help solve the difficulties encountered insegmentation. Approaches to delineation canbe broadly classified as boundary-based or re-gion-based.

In boundary-based delineation, an object de-scription is output in the form of a boundarysurface that separates the object from the back-ground. The boundary description may takethe form of a hard set of primitives (eg, points,polygons, surface patches, voxels) or a fuzzyset of primitives such that each primitive hasan assigned grade of “boundariness.”

In region-based delineation, an object de-scription is output in the form of the region oc-cupied by the object. The description may takethe form of a hard set of voxels or of a fuzzyset such that each voxel in the set has an as-signed grade of “objectness.” With the formermethod, each voxel in the set is considered tocontain 100% object material; with the lattermethod, this value may be anywhere from 0%to 100%.

Object knowledge usually facilitates recog-nition and delineation of that object. Paradoxi-cally, this implies that segmentation is requiredfor effective object segmentation. As we havenoted, segmentation is needed to perform mostof the preprocessing operations in an optimalfashion. It will be seen later that segmentationis essential for most visualization, manipula-tion, and analysis tasks. Thus, segmentation isthe most crucial among all 3D imaging opera-tions and also the most challenging.

Knowledgeable human beings usually out-perform computer algorithms in the high-leveltask of recognition. However, carefully designedcomputer algorithms outperform human beingsin achieving precise, accurate, and efficient de-lineation. Clearly, human delineation cannot ac-count for graded object composition. Most ofthe challenges in completely automating seg-mentation may be attributed to shortcomings incomputerized recognition techniques and thelack of delineation techniques that can handlegraded composition and hanging-togetherness.

There are eight possible combinations of ap-proaches to recognition and delineation, result-ing in eight different methods of segmentation.

With hard, boundary-based automatic seg-mentation, thresholding and isosurfacing aremost commonly used (29–32). In these tech-niques, a scene intensity threshold is specifiedand the surface that separates voxels with anintensity above the threshold from those withan intensity below the threshold is computed.Methods differ as to how the surface is repre-sented and computed and whether surfaceconnectedness is taken into account. The sur-face may be represented in terms of voxels,voxel faces, points, triangles, or other surfaceelements. If connectedness is not used, the sur-face obtained from a scene will combine dis-crete objects (eg, the femur and the patella inFig 3); with connectedness, each of the objectscan be represented as a separate surface (as-suming they are separated in the 3D scene). InFigure 6, the isosurface is connected and is rep-resented as a set of faces of voxels (29).

In addition to scene intensity threshold, in-tensity gradient has also been used in definingboundaries (33).

Another method of segmentation is fuzzy,boundary-based automatic segmentation. Con-cepts related to fuzzy boundaries (eg, connect-edness, closure, orientedness) that are well es-tablished for hard boundaries are difficult andas yet undeveloped. However, computationalmethods have been developed that identifyonly those voxels that are in the vicinity of theobject boundary and that assign each voxel agrade of “boundariness” (34,35). These meth-ods use scene intensity or intensity gradient todetermine boundary gradation (Fig 9).

In hard, boundary-based, human-assistedsegmentation, the degree of human assistanceranges from tracing the boundary entirely byhand (manual recognition and delineation) tospecifying only a single point inside the object


or on its boundary (manual recognition and au-tomatic delineation) (36–41). In routine clinicalapplications, manual boundary tracing is per-haps the most commonly used method. On theother hand, boundary detection methods re-quiring simple user assistance based on inten-sity (36,37) and gradient criteria (38–41) havebeen developed. However, these methods can-not be guaranteed to always work correctly inlarge applications.

There are many user-assisted methods be-sides those just described that require differentdegrees of human assistance for segmentationof each scene (42–48). In view of the inadequacyof the minimally user–assisted methods men-tioned earlier, much effort is currently being di-rected toward developing methods that take alargely manual approach to recognition and amore automatic approach to delineation. Thesemethods go under various names: active contoursor snakes (42–44), active surfaces (45,46), andlive-wire (live-lane) (47,48).

In active contour and active surface methods,a boundary is first specified (eg, by creating arectangle or a rectangular box close to theboundary of interest). The boundary is consid-ered to have certain stiffness properties. In ad-dition, the given scene is considered to exertforces on the boundary whose strength de-pends on the intensity gradients. For example,a voxel exerts a strong attractive force on theboundary if the rate of change in intensity ofthe voxel is high. Within this static mechanicalsystem, the initial boundary deforms and even-tually assumes a shape for which the combinedpotential energy is at a minimum. Unfortunately,the steady-state shape is usually impossible tocompute. Furthermore, whatever shape is ac-cepted as an alternative may not match with the

desired boundary, in which case further cor-rection of the boundary is needed. In assessingthe effectiveness of these segmentation meth-ods, it is important to evaluate their precision(repeatability) and efficiency (defined in terms ofthe number of scenes that can be segmented perunit time). Such evaluations have not been per-formed for methods described in the literature.

The principles underlying live-wire (live-lane) methods (47,48) are different from thosefor active boundary methods. In live-wire meth-ods, every pixel edge is considered to representtwo directed edges whose orientations are op-posite each other. The “inside” of the bound-ary is considered to be to the left of the di-rected edge, and its outside to the right. Eachdirected edge is assigned a cost that is inverselyrelated to the “boundariness” of the edge. Sev-eral local features are used to determine thecost and include intensity to the left (inside)and right (outside) as well as intensity gradientand its direction. In the 2D live-wire method,the user initially selects a point (pixel vertex)v

o on the boundary of interest. The computer

now shows a “live-wire” segment from vo to

the current mouse cursor position v. This seg-ment is an oriented path consisting of a con-nected sequence of directed pixel edges thatrepresents the shortest possible path from v

o to

v. As the user changes v through mouse move-ment, the optimal path is computed and dis-played in real time. If v is on or close to theboundary, the live wire “snaps” onto theboundary (Fig 10); v is now deposited and be-comes the new starting point and the processcontinues. Typically, two to five points are suf-ficient to segment a boundary (Fig 10). Thismethod and its derivatives are shown to be two

Figure 10. Live-wire segmentation. Section createdon the basis of data from an MR image of the footshows a live-wire segment representing a portionof the boundary of interest, which in this case out-lines the talus.

Figure 9. Fuzzy, boundary-based automatic seg-mentation. Rendition created with both intensityand gradient criteria shows the fuzzy boundariesof “bone” detected in the CT data from Figure 3.


to three times faster and statistically significantlymore repeatable than manual tracing (47). Its3D version (48) is about 3–15 times faster thanmanual tracing. Note that, in this method, rec-ognition is manual but delineation is automatic.

To our knowledge, no fuzzy, boundary-based,human-assisted methods have been describedin the literature.

The most commonly used hard, region-based,automatic method of segmentation is thresh-olding (Fig 11). A voxel is considered to belongto the object region if its intensity is at an upperor lower threshold or between the two thresh-olds. If the object is the brightest in the scene(eg, bone in CT scans), then only the lowerthreshold needs to be specified. The thresholdinterval is specified with a scene intensity his-togram in Figure 11b, and the segmented ob-ject is shown as a binary scene in Figure 11c.

Another commonly used method is cluster-ing (Fig 12). If, for example, multiple values as-sociated with each voxel are determined (eg,T2 and PD values), then a 2D histogram (alsoknown as a scatter plot) represents a plot ofthe number of voxels in the given 3D scene foreach possible value pair. The 2D histogram ofall possible value pairs is usually referred to asa feature space. The idea in clustering is thatfeature values corresponding to the objects ofinterest cluster together in the feature space.Therefore, to segment an object, one need onlyidentify and delineate this cluster. In other words,the problem of segmenting the scene becomesthe problem of segmenting the 2D scene repre-senting the 2D histogram. In addition to T2 andPD values, it is possible to use computed val-ues such as the rate of change in T2 and PD for

a. b. c.

Figure 11. Hard, region-based, automatic segmentation with use of thresholding. Once the desired scene isselected (a), an intensity interval is specified on a histogram (b). The segmented object is then depicted as abinary scene (c).

a. b. c.

Figure 12. Clustering. (a) Sections from an MR imaging scene with T2 (top) and PD (bottom) values assignedto voxels. (b) Scatter plot of the sections in a. A cluster outline for cerebrospinal fluid is indicated. (c) Segmentedbinary section demonstrates cerebrospinal fluid.


every voxel. In this case, the feature spacewould be four-dimensional. There are severalwell-developed techniques in the area of pat-tern recognition (49) for automatically identify-ing clusters, and these techniques have beenextensively applied to medical images (50–56).

One of the popular cluster identification meth-ods is the k–nearest neighbor (kNN) technique(49). Assume, for example, that the problem issegmenting the white matter (WM) region in a3D MR imaging scene in which the T2 and PDvalues have been determined for each voxel.The first step would be to identify two sets X

WM

and XNWM

of points in the 2D feature space thatcorrespond to white matter and non–white mat-ter regions. These sets of points will be used todetermine whether a voxel in the given scenebelongs to white matter. The sets are deter-mined with use of a “training” set. Suppose thatone or more scenes were previously segmentedmanually. Each voxel in the white matter andnon–white matter regions in each scene con-tributes a point to set X

WM or set X

NWM. The

next step would be to assign a value to k (eg, k= 7), which is a fixed parameter. The location Pin the feature space is determined for eachvoxel v in the scene to be segmented. In thiscase, the seven points from sets X

WM and X

NWM

that are “closest” to P are determined. If a ma-jority (>4) of these points are from X

WM, then v

is considered to be in white matter; otherwise, vdoes not belong to white matter. Note that thestep of obtaining X

WM and X

NWM need not be re-

peated for every scene to be segmented.Note also that thresholding is essentially

clustering in a one-dimensional feature space.All clustering methods have parameters whosevalues must be determined somehow. If theseparameters are fixed in an application, the ef-fectiveness of the method in routine process-ing cannot be guaranteed and some user assis-tance usually becomes necessary eventually.

Examples of other nonclustering methods havebeen described by Kamber (57) and Wells (58).

The simplest of the fuzzy, region-based, au-tomatic methods of segmentation is fuzzythresholding, which represents a generaliza-tion of the thresholding concept (Fig 13) (59).Fuzzy thresholding requires the specificationof four intensity thresholds (t

1–t

4). If the inten-

sity of a voxel v is less than t1 or greater than t

4,

the objectness of v is 0. If the intensity is be-tween t

2 and t

3, its objectness is 1 (100%). For

other intensity values, objectness lies between0% and 100%. Other functional forms have alsobeen used. Figure 14 shows a rendition of boneand soft tissue identified with fuzzy threshold-ing on the basis of the CT data from Figure 3.

Many of the clustering methods can be gen-eralized to output fuzzy object information. Forexample, in the kNN method described previ-ously, if a number m of the k points closest toP is from X

WM, then the objectness (“white mat-

ter–ness”) of v is m/k. Note that the fuzzythresholding described earlier is a form offuzzy clustering. One approach to more gener-alized fuzzy clustering is the fuzzy c-meansmethod (60). The application of this methodhas been investigated for segmenting brain tis-sue components in MR images (50). The ideais something like this: Suppose there are twotypes of tissues, white matter and gray matter,to be segmented in a 3D MR imaging scene,and that the feature space is 2D (composed ofT2 and PD values). Actually, three classes mustbe considered: white matter, gray matter, andeverything else. The task is to define threeclusters in the 2D scatter plot of the givenscene that correspond to these three classes.The set X of points to which the given scenemaps in the feature space can be partitionedinto three clusters in a large (although finite)number of ways. In the hard c-means method,the objective is to choose that particular clus-ter arrangement for which the sum (over allclusters) of the squared distances between thepoints in each cluster and the cluster center isthe smallest. In the fuzzy c-means method,each point in X is allowed to have an object-ness value between 0 and 1, making the num-ber of cluster arrangements infinite. The dis-tance in the criterion to be minimized is modifiedby the objectness value. Algorithms have beendescribed for both methods that are designedto find clusters that approximately minimizethe pertinent criterion.

As with hard clustering methods, the effective-ness of fuzzy clustering methods in routine appli-cations cannot be guaranteed because some userassistance on a per-scene basis is usually needed.

The simplest of the hard, region-based, human-assisted methods of segmentation is manualpainting of regions with a mouse-driven paint-brush (61). This method is an alternative tomanual boundary tracing.

Figure 13. Diagram illustrates fuzzy thresholding.


In contrast to this completely manual recog-nition and delineation scheme, there are meth-ods in which recognition is manual but delinea-tion is automatic. Region growing is a populartechnique in this group (62–64). At the outset,the user specifies a seed voxel within the ob-ject region with use of (for example) a mousepointer on a section display. A set of criteria forinclusion of a voxel in the object is also speci-fied; for example, (a) the scene intensity of thevoxel should be within an interval t

1 to t

2, (b) the

mean intensity of voxels included in the grow-ing region at any time during the growing pro-cess should be within an interval t

3 to t

4, and

(c) the intensity variance of voxels included inthe growing region at any time during the grow-ing process should be within an interval t

5 to t

6.

Starting with the seed voxel, the algorithm ex-amines its 3D neighbors (usually the closest six,18, or 26 neighbors) for inclusion. Those thatare included are marked so that they will notbe reconsidered for inclusion later. The neigh-bors of the voxels selected for inclusion are inturn examined, and the process continues untilno more voxels can be selected for inclusion.

If only criterion a in the preceding paragraphis used and t

1 and t

2 are fixed during the grow-

ing process, this method outputs essentially aconnected component of voxels satisfying a hardthreshold interval. Note also that for any com-bination of criteria a and b, or if t

1 and t

2 are not

fixed, it is not possible to guarantee that the setof voxels (object) O(v

l) obtained with a seed

voxel vl is the same as object O(v

2), where v

2 ≠ v

1

is a voxel in O(v1). This lack of robustness consti-

tutes a problem with most region-based methods.In the sense that the fuzzy region-based meth-

ods of segmentation described earlier eventu-

Figure 14. Fuzzy thresholding. Rendition of CTdata from Figure 3 with fuzzy thresholding depictsbone and soft tissue.

ally entail human assistance, they fall into thecategory of fuzzy, region-based, human-assistedmethods. A recent technique that was designedto make use of human assistance is the fuzzyconnected technique (65). In this method, rec-ognition is manual and involves pointing at anobject in a section display. Delineation is auto-matic and takes both graded composition andhanging-togetherness into account. It has beeneffectively applied in several applications in-cluding quantification of multiple sclerosis le-sions (66–69), MR angiography (70), and soft-tissue display for planning of craniomaxillofacialsurgery (71).

In the fuzzy connected technique, nearbyvoxels in the voxel array are thought of as hav-ing a fuzzy adjacency relation that indicatestheir spatial nearness. This relation, which var-ies in strength from 0 to 1, is independent ofany scene intensity values and is a nonincreas-ing function of the intervening distance. Fuzzyadjacency roughly captures the blurring char-acteristic of imaging devices.

Similarly, nearby voxels in a scene are thoughtof as having a fuzzy affinity relation that indicateshow they hang together locally in the same ob-ject. The strength of this relation (varying from0 to 1) between any two voxels is a function oftheir fuzzy adjacency as well as their scene in-tensity values. For example, this function maybe the product of the strength of their adjacencyand (l − | I[v

l] − I[v

2] |), where I[v

1] and I[v

2]

are the intensity values of voxels v1 and v

2

scaled in some appropriate way to the rangebetween 0 and 1. Affinity expresses the degreeto which voxels hang together to form a fuzzyobject. Of course, the intent is that this is a localproperty; voxels that are far apart will havenegligible affinity as defined in this function.The real “hanging-togetherness” of voxels in aglobal sense is captured through a fuzzy rela-tion called fuzzy connectedness. A strength ofconnectedness is assigned to each pair ofvoxels (v

l, v

2) as follows: There are numerous

possible paths between two voxels v1 and v

2,

any one of which consists of a sequence ofvoxels starting from v

1 and ending on v

2. Succes-

sive voxels are nearby and have a certain degreeof adjacency. The “strength” of a path is simplythe smallest of the affinities associated withpairs of successive voxels along the path. Thestrength of connectedness between v

1 and v

2 is

simply the largest of the strengths associatedwith all possible paths between v

1 and v

2. A

fuzzy object is a pool of voxels together with amembership (between 0 and 1) assigned toeach voxel that represents its objectness. Thepool is such that the strength of connectedness


between any two voxels in the pool is greaterthan a small threshold value (typically about0.1) and the strength between any two voxels(only one of which is in the pool) is less thanthe threshold value. Obviously, computing fuzzyobjects even for this simple affinity function iscomputationally impractical if we proceed straightfrom the definitions. However, the theory al-lows us to simplify the complexity considerablyfor a wide variety of affinity relations so thatfuzzy object computation can be done in prac-tical time (about 15–20 minutes for a 256 × 256× 64 3D scene (16 bits per voxel) on a SPARC-station 20 workstation (Sun Microsystems, Moun-tain View, Calif). A wide spectrum of applica-tion-specific knowledge of image characteristicscan be incorporated into the affinity relation.

Figure 15 shows an example of fuzzy con-nected segmentation (in 3D) of white matter,

gray matter, cerebrospinal fluid, and multiplesclerosis lesions in a T2, PD scene pair. Figure16a shows an MIP rendition of an MR angiogra-phy data set, whereas Figure 16b demonstratesa rendition of a 3D fuzzy connected vessel treedetected from a point specified on the vessel.

There are a number of challenges associatedwith segmentation, including (a) developinggeneral segmentation methods that can be eas-ily and quickly adapted to a given application,(b) keeping human assistance required on a perscene basis to a minimum, (c) developing fuzzymethods that can realistically handle uncertain-ties in data, and (d) assessing the efficacy ofsegmentation methods.

■■■■■ VISUALIZATIONVisualization operations create renditions ofgiven scenes or object systems. Their purposeis to create renditions from a given set of

a. b.

c. d. e.

Figure 15. Fuzzy connected segmentation. (a, b) Sections from an MR imaging scene with T2 (a) and PD (b)values assigned to voxels. (c–e) Sections created with 3D fuzzy connected segmentation demonstrate theunion of white matter and gray matter objects (c), the cerebrospinal fluid object (d), and the union of multi-ple sclerosis lesions (e) detected from the scene in a and b.


scenes or objects that facilitate the visual per-ception of object information. Two approachesare available: scene-based visualization and ob-ject-based visualization.

●●●●● Scene-based VisualizationIn scene-based visualization, renditions are cre-ated directly from given scenes. Within this ap-proach, two further subclasses may be identi-fied: section mode and volume mode.

Section Mode.—Methods differ as to what con-stitutes a “section” and how this information isdisplayed. Natural sections may be axial, coro-nal, or sagittal; oblique or curved sections arealso possible. Information is displayed as a mon-tage with use of roam-through (fly-through) andgray scale and pseudocolor. Figure 17 shows amontage display of the natural sections of a CT

a. b.

Figure 16. Fuzzy connected segmentation. (a) Three-dimensional maximum-intensity-projection(MIP) rendition of an MR angiography scene. (b) MIP rendition of the 3D fuzzy connected vessels de-tected from the scene in a. Fuzzy connectedness has been used to remove the clutter that obscuresthe vasculature.

Figure 17. Montage display of a 3D CT scene of the head.


scene. Figure 18 demonstrates a 3D display–guided extraction of an oblique section from aCT scene of a pediatric patient’s head. This re-sectioning operation illustrates how visualiza-tion is needed to perform visualization itself.Figure 19 illustrates pseudocolor display withtwo sections from a brain MR imaging study ina patient with multiple sclerosis. The two sec-tions, which represent approximately the samelocation in the patient’s head, were taken from3D scenes that were obtained at different timesand subsequently registered. The sections areassigned red and green hues. The displayshows yellow (produced by a combination of

red and green hues) where the sections matchperfectly or where there has been no change(for example, in the lesions). At other places, ei-ther red or green is demonstrated.

Volume Mode.—In volume mode visualiza-tion, information may be displayed as surfaces,interfaces, or intensity distributions with use ofsurface rendering, volume rendering, or MIP. Aprojection technique is always needed to movefrom the higher-dimensional scene to the 2Dscreen of the monitor. For scenes of four ormore dimensions, 3D “cross sections” mustfirst be determined, after which a projectiontechnique can be applied to move from 3D to

19a. 19b.

Figures 18, 19. (18) Three-dimensional display–guided extraction of an oblique section from CTdata obtained in a patient with a craniofacial disorder. A plane is selected interactively by means ofthe 3D display to indicate the orientation of the section plane (left). The section corresponding to theoblique plane is shown on the right. (19) Pseudocolor display. (a) Head MR imaging sections obtainedat different times are displayed in green and red, respectively. Where there is a match, the compositeimage appears yellow. Green and red areas indicate regions of mismatch. (b) On the same compositeimage displayed after 3D scene-based registration, green and red areas indicate either a registrationerror or a change in an object (eg, a lesion) over the time interval between the two acquisitions.

18.


2D. Two approaches may be used: ray casting(34), which consists of tracing a line perpen-dicular to the viewing plane from every pixelin the viewing plane into the scene domain, orvoxel projection (72), which consists of directlyprojecting voxels encountered along the pro-jection line from the scene onto the viewingplane (Fig 20). Voxel projection is generallyconsiderably faster than ray casting; however,either of these projection methods may be usedwith any of the three rendering techniques(MIP, surface rendering, volume rendering).

In MIP, the intensity assigned to a pixel in therendition is simply the maximum scene inten-sity encountered along the projection line (Fig16a) (73,74). MIP is the simplest of all 3D ren-dering techniques. It is most effective whenthe objects of interest are the brightest in thescene and have a simple 3D morphology and aminimal gradation of intensity values. Contrastmaterial–enhanced CT angiography and MR an-giography are ideal applications for this method;consequently, MIP is commonly used in theseapplications (75,76). Its main advantage is thatit requires no segmentation. However, theideal conditions mentioned earlier frequently gounfulfilled, due (for example) to the presence ofother bright objects such as clutter from surfacecoils in MR angiography, bone in CT angiogra-phy, or other obscuring vessels that may not beof interest. Consequently, some segmentationeventually becomes necessary.

In surface rendering (77), object surfaces areportrayed in the rendition. A threshold intervalmust be specified to indicate the object of in-terest in the given scene. Clearly, speed is ofthe utmost importance in surface rendering be-cause the idea is that object renditions are cre-

ated interactively directly from the scene as thethreshold is changed. Instead of thresholding,any automatic, hard, boundary- or region-basedmethod can be used. In such cases, however,the parameters of the method will have to bespecified interactively, and the speed of seg-mentation and rendition must be sufficient tomake this mode of visualization useful. Althoughrendering based on thresholding can presentlybe accomplished in about 0.03–0.25 secondson a Pentium 300 with use of appropriate algo-rithms in software (61), more sophisticated seg-mentation methods (eg, kNN) may not offer in-teractive speed.

The actual rendering process consists ofthree basic steps: projection, hidden part re-moval, and shading. These steps are needed toimpart a sense of three-dimensionality to therendered image that is created. Additional cuesfor three-dimensionality may be provided bytechniques such as stereoscopic display, mo-tion parallax by rotation of the objects, shad-owing, and texture mapping.

If ray casting is used as the method of pro-jection, hidden part removal is performed bystopping at the first voxel encountered alongeach ray that satisfies the threshold criterion(78). The value (shading) assigned to the pixelin the viewing plane that corresponds to the rayis determined as described later. If voxel pro-jection is used, hidden parts can be removedby projecting voxels from the farthest to theclosest (with respect to the viewing plane) andalways overwriting the shading value, whichcan be achieved in a number of computationallyefficient ways (72,79–81).

Figure 20. Schematic illustrates pro-jection techniques for volume modevisualization. Projections are createdfor rendition either by ray casting fromthe viewing plane to the scene or byprojecting voxels from the scene tothe viewing plane.


The shading value assigned to a pixel p inthe viewing plane depends on the voxel v thatis eventually projected onto p. The faithfulnesswith which this value reflects the shape of thesurface around v largely depends on the surfacenormal vector estimated at v. Two classes ofmethods are available for this purpose: object-based methods and scene-based methods. Inobject-based methods (82,83), the vector is de-termined purely from the geometry of the shapeof the surface in the vicinity of v. In scene-basedmethods (78), the vector is considered to be thegradient of the given scene at v; that is, the di-rection of the vector is the same as the directionin which scene intensity changes most rapidlyat v. Given the normal vector N at v, the shad-ing assigned to p is usually determined as [f

d(v,

N, L) + fs(v, N, L, V)] f

D(v), where f

d is the dif-

fuse component of reflection, fs is the specular

component, fD is a component that depends on

the distance of v from the viewing plane, and Land V are unit vectors indicating the directionof the incident light and of the viewing rays. Thediffuse component is independent of the view-ing direction but depends solely on L (as a cosineof the angle between L and N). It captures thescattering property of the surface, whereas thespecular component captures surface shininess.The specular component is highest in the direc-tion of ideal reflection R whose angle with N isequal to the angle between L and N. This reflec-tion decreases as a cosine function on either sideof R. By weighting the three components in dif-ferent ways, different shading effects can beachieved.

In scene-based surface rendering, a hard ob-ject is implicitly created and rendered “on thefly” from the given scene. In scene-based volumerendering, a fuzzy object is implicitly created andrendered on the fly from the given scene. Clearly,surface rendering becomes a special case of vol-ume rendering. Furthermore, volume renderingin this mode is generally much slower than sur-face rendering, typically requiring 3–20 secondseven on specialized hardware rendering engines.

The basic idea in volume rendering is to as-sign an opacity from 0% to 100% to every voxelin the scene. The opacity value is determinedon the basis of the objectness value at the voxeland of how prominently one wishes to portraythis particular grade of objectness in the rendi-tion. This opacity assignment is specified inter-actively by way of an opacity function (Fig 13),wherein the vertical axis indicates percentage

of opacity. Every voxel is now considered totransmit, emit, and reflect light. The goal is todetermine the amount of light reaching everypixel in the viewing plane. The amount of lighttransmitted depends on the opacity of the voxel.Light emission depends on objectness and henceon opacity: The greater the objectness, the greaterthe emission. Similarly, reflection depends onthe strength of the surface that is present: Thegreater the strength, the greater the reflection.

Like surface rendering, volume renderingconsists of three basic steps: projection, hid-den part removal, and shading or compositing.The principles underlying projection are identi-cal to those described for surface rendering.

Hidden part removal is much more compli-cated for volume rendering than for surface ren-dering. In ray casting, a common method is todiscard all voxels along the ray from the viewingplane beyond a point at which the “cumulativeopacity” is above a high threshold (eg, 90%) (84).In voxel projection, a voxel can also be discardedif the voxels surrounding it in the direction ofthe viewing ray have “high” opacity (35).

The shading operation, which is more ap-propriately termed compositing, is also morecomplicated for volume rendering than for sur-face rendering. Compositing must take into ac-count all three components: transmission, re-flection, and emission. One may start from thevoxel farthest from the viewing plane along eachray and work toward the front, calculating theoutput light for each voxel. The net light out-put by the voxel closest to the viewing plane isassigned to the pixel associated with the ray.Instead of using this back-to-front strategy, one

Figure 21. Scene-based volume rendering withvoxel projection. Rendition of knee CT data fromFigure 3 shows bone, fat, and soft tissue.


may also make calculations from front to back,which has actually been shown to be faster (35).

In volume rendering (as in surface render-ing), voxel projection is substantially faster thanray casting. Figure 21 shows the CT knee dataset illustrated in Figure 3 as rendered with thismethod. Three types of tissue—bone, fat, andsoft tissue—have been identified.

●●●●● Object-based VisualizationIn object-based visualization, objects are firstexplicitly defined and then rendered. In difficultsegmentation situations, or when segmentationis time consuming or involves too many param-eters, it is impractical to perform direct scene-based rendering. The intermediate step of com-pleting object definition then becomes necessary.

Surface Rendering.—Surface renderingmethods take hard object descriptions as inputand create renditions. The methods of projec-tion, hidden-part removal, and shading are simi-lar to those described for scene-based surfacerendering, except that a variety of surface de-scription methods have been investigated us-ing voxels (72,79,81), points, voxel faces (29,80,85,86), triangles (30,37,87), and other sur-face patches. Therefore, projection methodsthat are appropriate for specific surface elementshave been developed. Figure 22a shows a ren-dition, created with use of voxel faces on thebasis of CT data, of the craniofacial skeleton in apatient with agnathia. Figure 8 shows renditionsof the bones of the foot created by way of thesame method on the basis of MR imaging data.

Volume Rendering.—Volume renderingmethods take as input fuzzy object descriptions,which are in the form of a set of voxels whereinvalues for objectness and a number of other pa-rameters (eg, gradient magnitude) are associ-ated with each voxel (35). Because the objectdescription is more compact than the originalscene and additional information for increasingcomputation speed can be stored as part of theobject description, volume rendering based onfuzzy object description can be performed atinteractive speeds even on personal computerssuch as the Pentium 300 entirely in software.In fact, the rendering speed (2–15 sec) is nowcomparable to that of scene-based volume ren-dering with specialized hardware engines. Fig-ure 22b shows a fuzzy object rendition of thedata set in Figure 22a. Figure 23a shows a ren-dition of craniofacial bone and soft tissue, bothof which were defined separately with use ofthe fuzzy connected methods described ear-lier. Note that if one uses a direct scene-basedvolume rendering method with the opacityfunction illustrated in Figure 13, the skin be-comes indistinguishable from other soft tissuesand always obscures the rendition of muscles(Fig 23b).

●●●●● Misconceptions in VisualizationSeveral inaccurate statements concerning visu-alization frequently appear in the literature.The following statements are seen most often:

a. b.

Figure 22. Object-based visualization of the skull in a child with agnathia. (a) Surface-rendered im-age. (b) Subsequent volume-rendered image was preceded by the acquisition of a fuzzy object repre-sentation with use of fuzzy thesholding (cf Fig 13).


“Surface rendering is the same as thresh-olding.”—Clearly, thresholding is only one—indeed, the simplest—of the many availablehard region- and boundary-based segmentationmethods, the output of any of which can besurface rendered.

“Volume rendering does not require seg-mentation.”—Although volume rendering is ageneral term and is used in different ways, thestatement is false. The only useful volume ren-dering or visualization technique that requiresno segmentation is MIP. The opacity assignmentschemes illustrated in Figure 13 and describedin the section entitled “Scene-based Visualiza-tion” are clearly fuzzy segmentation strategiesand involve the same problems that are en-countered with any segmentation method. It isuntenable to hold that opacity functions suchas the one shown in Figure 13 do not representsegmentation while maintaining that the mani-festation that results when t

1 = t

2 and t

3 = t

4 (cor-

responding to thresholding) does representsegmentation.

“The term volume rendering may be usedto refer to any scene-based rendering tech-nique as well as object-based renderingtechniques.”—The meaning of the term as usedin the literature varies widely. In one sense, itcan also apply to the section mode of visualiza-tion. It is better to use volume rendering to referto fuzzy object rendering, whether performedwith scene-based or object-based methods, butnot to hard object rendering methods.

There are many challenges associated withvisualization. First, preprocessing operations

(and, therefore, visualization operations) can beapplied in many different sequences to achievethe desired result. For example, the filtering-in-terpolation-segmentation-rendering sequencemay produce renditions that are significantlydifferent from those produced by interpolation-segmentation-filtering-rendering. With the largenumber of different methods possible for eachoperation and the various parameters associatedwith each operation, there are myriad ways ofachieving the desired results. Figure 24 showsfive images derived from CT data that werecreated by performing different operations. Sys-tematic study is needed to determine whichcombination of operations is optimal for a givenapplication. Normally, the fixed combinationprovided by the 3D imaging system is assumedto be the best for that application. Second, ob-jective comparison of visualization methodsbecomes an enormous task in view of the vastnumber of ways one may reach the desired goal.A third challenge is achieving realistic tissuedisplay that includes color, texture, and surfaceproperties.

■■■■■ MANIPULATIONManipulation operations are used primarily tocreate a second object system from a given ob-ject system by changing objects or their rela-tions. The main goal of these operations is tosimulate surgical procedures on the basis of pa-tient-specific scene data and to develop aids forinterventional and therapy procedures. Comparedwith preprocessing and visualization, manipula-tion is in its infancy; consequently, it will notbe discussed in as much detail. Two classes ofoperations are being developed: rigid manipu-lation and deformable manipulation.

a. b.

Figure 23. Visualization withvolume rendering. (a) Object-based volume-rendered imagedemonstrates bone and soft-tis-sue structures (muscles) that hadbeen detected earlier as sepa-rate fuzzy connected objects ina 3D craniofacial CT scene. Theskin is essentially “peeled away”because of its weak connect-edness to muscles. (b) Scene-based volume-rendered versionof the scene in a was acquiredwith use of the opacity function(cf Fig 13) separately for boneand soft tissue. The skin has be-come indistinguishable frommuscles because they have simi-lar CT numbers and hence ob-scures the rendition of themuscles.


●●●●● Rigid ManipulationOperations to cut, separate, add, subtract, move,and mirror objects and their components havebeen developed with use of both hard and fuzzyobject definitions (81,88–91). In rigid manipu-lation, the user interacts directly with an object-based surface or volume rendition of the objectsystem (Fig 25). Clearly, an operation must beexecutable at interactive speeds to be practical.This is possible with both hard and fuzzy ob-ject definitions (81,91) on a personal computersuch as a Pentium 300.

●●●●● Deformable ManipulationOperations to stretch, compress, bend, and soon are being developed. Mechanical modelingof soft-tissue structures including muscles, ten-

dons, ligaments, and capsules is complicatedbecause the forces that they generate and theirbehavior under external forces are difficult todetermine, especially in a patient-specific fash-ion. Therefore, in past attempts at modeling,properties of soft tissues have been taken intoconsideration in a generic but not patient-spe-cific fashion. Generic models based on localdeformations are used as an aid in facial plasticsurgery (92) quite independent of the underly-ing bone and muscle, treating only the skin sur-face. The use of multiple layers—skin, fatty tis-sue, muscle, and bone that does not move—hasbeen explored in different combinations tomodel facial expression animation (93–95). Al-though attempts have been made to model softtissue in this fashion and to duplicate its mechani-cal properties (96), no attempt seems to havebeen made to integrate hard-tissue (bone) changeswith the soft-tissue modifications in a model.Reasons include the lack of adequate visualiza-tion tools and the lack of tools to simulate os-teotomy procedures or integrate soft-tissue mod-els with hard-tissue changes.

The area of deformable manipulation is openfor further research. Because most of the tis-sues in the body are deformable and movableand object information in images is inherentlyfuzzy, basic fuzzy mechanics theories and algo-rithms need to be developed to carry out pa-tient-specific object manipulation and analysis.

■■■■■ ANALYSISThe main purpose of analysis operations is togenerate a quantitative description of the mor-phology, architecture, and function of the ob-ject system from a given set of scenes or objectsystem.

Figure 24. Preprocess-ing and visualization op-erations. Renditions fromCT data were createdwith use of five differ-ent preprocessing andvisualization operations.

Figure 25. Rigid manipulation. Rendition cre-ated from CT data obtained in a child demon-strates rigid manipulation for use in surgicalplanning. This “virtual surgery” mimics an os-teotomy procedure used in craniomaxillofacialsurgery to advance the frontal bone.


The goal of many 3D imaging applications isanalysis of an object system. Although visual-ization is used as an aid, it may not be an end initself. As such, many of the current application-driven works are related to analysis. Like, otheroperations, analysis operations may be classi-fied into two groups: scene-based analysis andobject-based analysis.

●●●●● Scene-based AnalysisIn scene-based analysis, quantitative descriptionsare based directly on scene intensities and in-clude region-of-interest statistics as well as mea-surements of density, activity, perfusion, andflow. Object structure information derived fromanother modality is often used to guide the se-lection of regions for these measurements.

●●●●● Object-based AnalysisIn object-based analysis, quantitative descrip-tion is obtained from an object on the basis ofmorphology, architecture, change over time,relationships with other objects in the system,and changes in these relationships. Examplesof measurements obtained in this manner in-clude distance, length, curvature, area, volume,kinematics, kinetics, and mechanics.

Object information in images is fuzzy; there-fore, the challenge is to develop fuzzy morphom-etry and mechanics theories and algorithms toenable realistic analysis of the object information.

■■■■■ DIFFICULTIES IN 3D IMAGINGThere are two main types of difficulties associ-ated with 3D imaging: those related to objectdefinition and those related to validation. Theformer have already been discussed in detail(see “Preprocessing”). Difficulties related tovalidation are discussed in this section.

Validation may be either qualitative or quan-titative. The purpose of qualitative validation isto compare visualization methods for a giventask. Observer studies and receiver operatingcharacteristic analysis may be used (97). A ma-jor challenge is how to select a small numberof methods for formal receiver operating char-acteristic analysis from among the numerouscombinations of operations and methods andtheir parameter settings.

The purpose of quantitative validation is toassess the precision, accuracy, and efficiency ofthe measurement process.

Precision refers to the reliability of themethod and is usually easy to establish by re-peating the measurement process and assess-ing variation using coefficient of variation, cor-relation coefficient, κ statistic, and analysis ofvariance. All steps that involve subjectivity must

be repeated (including, for example, how thepatient is positioned in the scanner).

Accuracy refers to how the measurementagrees with truth. Establishing recognition ac-curacy requires histologic assessment of objectpresence or absence for small objects. For large(anatomic) objects, an expert reader can pro-vide truth. Receiver operating characteristicanalysis can then be applied.

Establishing delineation accuracy requires apoint-by-point assessment of object grade. Truthis very difficult to establish. Typically, the fol-lowing surrogates of truth are used: physicalphantoms, mathematic phantoms, manual (ex-pert) delineation, simulation of mathematicalobjects that are then imbedded in actual images,and comparison with a process whose accuracyis known.

Efficiency refers to the practical viability ofthe method—for example, in terms of the num-ber of studies that can be processed per hour.This variable has two components: computertime and operator time. Computer time is notcrucial so long as it remains within the boundsof practicality. However, operator time is cru-cial in determining whether a method is practi-cally viable regardless of its precision or accu-racy. This aspect of validation is usually ignored,but it should be conducted and its statisticalvariation analyzed and reported.

■■■■■ CONCLUSIONSAlthough 3D imaging poses numerous chal-lenges for mathematicians, engineers, physicists,and physicians, it is an exciting technology thatpromises to make important contributions in awide range of disciplines in years to come.

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