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Automatic Identification of Ambiguous Automatic Identification of Ambiguous Prostate Capsule Boundary Lines Using Prostate Capsule Boundary Lines Using Shape Information and Least Squares Shape Information and Least Squares

Curve Fitting TechniqueCurve Fitting Technique

Rania Hussein, Ph.D.Rania Hussein, Ph.D.Department of Computer EngineeringDepartment of Computer Engineering

DigiPen Institute of Technology DigiPen Institute of Technology Seattle, WASeattle, WA

Frederic (Rick) D. McKenzie, Ph.D.Frederic (Rick) D. McKenzie, Ph.D.Department of Electrical and Computer EngineeringDepartment of Electrical and Computer Engineering

Old Dominion UniversityOld Dominion University Norfolk, VANorfolk, VA

fmckenzi@ece.odu.edufmckenzi@ece.odu.edu

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Old Dominion UniversityOld Dominion University• Located near Virginia Beach

– 3 hours south of Washington, DC– Over 25,000 students

• Engineering College has over 100 Faculty• Electrical & Computer Engineering Dept.

– 26 faculty members– 240 undergraduate students– 140 graduate students: 50 PhD, 90 Masters– 2003 R&D Expenditure National Ranking of ECE at

ODU according to NSF: 29– 2004 R&D Expenditure National Ranking of ECE at

ODU according to NSF: 28

Staff and ActivitiesStaff and Activities

• Enterprise Center, Old Dominion University

• 12 Faculty, ~55 research & admin staff

• Multidisciplinary: activities include faculty and students from all six academic colleges

• ~$7.5M in funded research in FY 2005

• Modeling & Simulation Graduate Programs– Over 100 Masters and Doctorate students

Virginia Modeling Analysis and Simulation CenterVirginia Modeling Analysis and Simulation Center

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OutlineOutline

• Motivation

• Problem definition

• Background

• Approach

• Results

• Conclusion

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MotivationMotivation• Assessment of different surgical

approaches to prostatectomy using objective parameters (such as extra-capsular tissue coverage)

• Reconstruct the prostate capsule and its extra-capsular tissue from excised specimen histology

• Capsule contour is needed and is currently drawn manually by the pathologist

• Subjective and therefore may affect the accuracy of the quantitation results

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Problem definitionProblem definition

• This research focuses on developing an algorithm that automatically identifies this capsule contour

• Validation is performed by comparing with the hand-drawn contour of the pathologist

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Problem DefinitionProblem Definition

• Slices are serially cut from apex to base at precise and parallel 5mm intervals

• Sections of four microns in thickness are mounted on large glass slides stained with Eosin and Hematoxilin

The capsule is manually marked by a pathologist as shown by the dashed line in the figure

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BackgroundBackground

• The prostate capsule is a fibromuscular band of transversely oriented collagenous fibers, and it lies between the parenchymal contour and the periprostatic tissues

Epithelial cells

Parenchymal contour

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Prostatic tissues that can be Prostatic tissues that can be automatically classifiedautomatically classified

• Diamond et al [19] used whole-mount radical prostatectomy histology captured at 40x magnification (58k x 42k image size)

• Subimage sizes of 100x100 for processing

• The authors were able to correctly classify 79.3% of tissue in subregions

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Detectable ConstraintsDetectable Constraints• The prostate capsule has a mean thickness of 0.5

to 2 mm [Sattar et al.]

• However, it is unrecognizable in areas – Naturally occurring intrusion of muscle into the prostate gland at

the anterior apex.– Fusion of extraprostatic connective tissue with the prostate gland

at its base.

ParenchymalContour

Outer Contour

CapsuleContour

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Limacon shape equationLimacon shape equation• Limacon equation is r = b + a cos θ

(a) (b) (c)

Limacon curves (a) when a< b, (b) when a<b<2a, and (c) when 2a<=b.

• To take rotation into consideration, the equation becomes r = b + a cos (θ+Φ)

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Least squares algorithmLeast squares algorithmAssuming that we have a number n of discrete data (x1,y1),

(x2,y2), …(xn,yn) and f(x) is a function for fitting a curve. Therefore, f(x) has the deviation (error) d from each data point, i.e. d1 = y1-f(x1), d2 = y2-f(x2), …, dn = yn-f(xn)

Using Limacon Equation• Select range of values for the center of the curve (cx,cy)• Select range of values for the curve parameters (a, b)• Select range of values for the curve rotation angle (theta)

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a) Arrows point to the detected parts of the prostate capsule, (b) Arrow points to the curve representing the prostate shape located as close as possible to the capsule parts.

a b

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Merging arcs (least squares)Merging arcs (least squares)

• Once the curve is positioned, this shape curve is combined with the true capsule segments

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Curve Constraint ViolationCurve Constraint Violation

• The generated curve can violate the constraints– Prostate capsule is

typically located between the parenchymal contour and the prostate perimeter

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• Flood fill algorithm used to relocate the curve sections that violate constraints– New points are

generated between the 2 contours

– Least square algorithm executed again for better results

Curve Constraint AdjustmentCurve Constraint Adjustment

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Experiment ResultsExperiment Results

• 13 specimens were used • Tested on Pentium 4

machines with dual processors of 3.4GHz and 1.00 GB of RAM

• Parts where capsule is expected to exist (as figure shows) were manually outlined.

• Tested using 3 shape equations: Circle, Limacon, and ellipse

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Least squares testing exampleLeast squares testing example

a) Capsule parts b) LS Generated curve c) Arcs merging

d) New points generated by flood-fill algorithm

e) Curve generated after the 2nd run of LS f) Final curve after merging arcs from

the 2nd run

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Performance evaluationPerformance evaluation

• Used both the root mean square error RMSE and the percentage of error

Where n is the number of points in the curve,di is the min distance from point i in the curve to the reference curve.

Where m is the number of points in the reference curve,

di is the min distance from point i in the reference curve to the

curve

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Performance evaluationPerformance evaluation

• Thresholds considered in our study are equal to 1%, 1.5%, and 2% of the number of pixels of the image diagonal.

Figure illustrates the size that each threshold contributes to the actual size of a prostate slice. The squares that appear on the top left represent the number of pixels that are equal to 1%, 1.5%, 2% of the image diagonal respectively.

The %matching between our generated curve and the reference curve is calculated where,

%matching = 1- percentage error

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ResultsResults

0

5

10

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circle limacon ellipse

Shape

RMSE of least squares algorithm

RMSE

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ResultsResults

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50

60

70

80

90

circle limacon ellipse

Shapes

Percentage of matching between the calculated curve and the optimal curve at 0.01 tolerance for the least squares algorithms

%matching

40

50

60

70

80

90

circle limacon ellipse

Shape

Percentage of matching between the calculated curve and the optimal curve at 0.015 tolerance for the least squares algorithm

%matching

40

50

60

70

80

90

circle limacon ellipse

Shape

Percentage of matching between the calculated curve and the optimal curve at 0.02 tolerance for the least squares algorithm

%matching

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How to improve the resultsHow to improve the results

• Use more complex shape equations with greater degree of freedom

• A standard shape of a prostate slice can be defined by

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ConclusionConclusion

• The algorithm provides better results as better shape equations are used.

• The least squares algorithm gave better results on average than a GHT algorithm.

• GHT achieved zero error within our threshold on one of the specimens, which shows that more complex equations with greater degree of freedom is likely to give better results in the GHT.

• The combination of the two algorithms within the overall process allows a tradeoff between faster processing time and smaller errors in using more complicated and flexible prostate shapes.

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Thank You!