ifsr feature correspondence

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Feature Correspondence

Wright State University

Image Registration and Fusion Systems


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Point pattern matching:

1) scene coherence2) clustering

Line matching

Region matching:1) shape matching

2) relaxation labeling

3 chamfer matchin

Template matching:

1) Similarity measures

2

oarse-to- ne met o s


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Problem: Given two sets of points,

determine the correspondence between them. Information about only the locations of the

oints is available.

The points may contain positional error.

Some points may exist in only one of the sets.

We will only consider the case where the two

point sets are related by the affine

transformation.

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Point pattern matching using

scene coherenceIf three points in the two sets are aligned, because of the

scene coherence, the remaining points in the two sets will

also align.RANSAC Algorithm: Find three corresponding points.

.and find the affine transformation that aligns them.

2. Count the number of other points in the two sets

that also align with the obtained transformation.. , .

Otherwise, go to step 1.

To speed up the search, limit the point combinations to

those falling on the convex-hulls or the minimum-spanningtrees of the two sets.

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clusteringAlgorithm:

1. Create accumulators a[ ] f[ ] and initialize theentries to 0.

2. From point triples in the two sets calculate a

X=ax+by+c,

Y=dx+ey+f.

3. Increment entries a of accumulators a[ ] f[ ],

.

.

.

respectively, by 1.

4. Repeat Steps 2 and 3 a sufficiently large number oftimes.

.

. f[ ]. They show parameters a fof the registration. f

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affine invariance

transformation, knowing three corresponding

points in the two sets (p1,q1), (p2,q2), (p3,q3), pp1 p3

the relation between corresponding points

(p,q

) in the sets can be written as

p2

=

q = q1 + a1(q2 q1) + a2(q3 q1)q

q1q3

q2

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affine invarianceAlgorithm:

1. Create two 2-D accumulator arrays H1

[ ]and H2[ ].

2. Select three oints in set 1 and for eachadditional point in set 1 calculate a1 and a2and increment entry [a1,a2] ofH1[ ] by 1.

3. Select three points in set 2 and for each H1

additional point in set 2 calculate a1 and a2and increment entry [a1,a2] ofH2[ ] by 1.

4. Find the similarity between H1 and H2. If

t e s m ar ty s su c ent y g , ta e t epoint triples selected in Steps 2 and 3 ascorresponding points and stop. Otherwise,

H2

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.


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Assum tion: Ima es are related b a

rigid transformation (unknowntranslation and rotation).

Algorithm:

1. Find the rotational difference.

2. Correct the orientation of set 2 withres ect to set 1.

3. Find the translational differencebetween the line sets.

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h e m tchin

Fourier descriptors

Shape matrices

Chamfer matching

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{(xi,yi): i=0,,N-1}, thexy coordinates of the

samples from a periodic signal. Letting

= =, ,

computed from

,)/2exp(1 1

0

N

i

ik NkijN

zc k=0,,N-1

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Given boundary pixels {(xi,yi): i=0,,N-1}, the (p+q)th

order moment is defined by

1N

i

q

i

p

ipq fyxm

The (p+q)th order central moment of the boundary is

defined by

0i

1

Invariant moments:i

qi

p

0i

ipq f)yy()xx(u

1

20

02

.

a7 = (3u21 u03)

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is independent of its position, orientation, andscale.

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Denote regions in the reference image by

ai: = ,,m an reg ons n t e sense mage y

{bi:i=1,,n}. Ifais denote objects and bis denote labels, the

labels for the objects such that a compatibilitycondition is satisfied.

Initially assign labels to the objects with probabilities

Set of objects

proportional to their similarities.

Pi(bj): similarity between regions ai and bj.

Iteratively revise the label probabilities until they

converge to e t er or .Set of labels

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Given two binary images with translational

differences:1. Initially position the sensed image within

the reference image at (i,j) based on some.

2. Determine the similarity between the twoimages using distances of closest objectpoints.

Reference Sensed

3. Reposition the sensed image within thereference image at the eight neighbors of(i,j) and determine the image similarities atthese ei ht ositions.

4. If highest similarity is obtained when sensedimage is at (i,j), stop. Otherwise, move thesensed image to the neighbor of(i,j) that

Initialization of

sensed in reference

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Step 2.


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Given a binar ima e assi n to a

background pixel a value proportionalto its distance to the object point closest

.

To speed up the computations, integer

distances may be used, but note that Distance transform of asingle point

integer distances involve errors and

make distances dependent on the

.

Isovalued distances

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rotationally invariant, useactual Euclidean distances.

Distance transform in its

Euclidean distance transform of a single point and the

isovalued distances.

current form is very

sensitive to noise.

Eulidean distance transformEuclidean distance transform

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Instead of saving a

single distance at a pixel,

distances.

This can be implemented

Circle Circle + 5 points

image with a Gaussian

and inverting the values.

New DT of circle + 5

points

Traditional DT of circle +

5 points

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the images are no longer binary.

m y me su es

Sum of absolute differences Cross-corre at on coe c ent

Mutual information

Gaussian weighted templates

Coarse-to-fine a roaches

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differences, shift one image over the other and at eachshift position determine the similarity between the two.

Sum of absolute differences

Cross-correlation coefficient = mean

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Create a 2-D histogram with entry [a,b]

Template Window

a b

with intensity a that align with intensity b in thewindow.

x x

Divide the counts by the number of pixels in

template to obtain joint probabilities. b

2-D

histogram

, a

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Instead of treatin all ixels in a

template similarly, give higher weightsto pixels that are closer to the template

center.

This makes the process less dependenton image orientation when using rectangular templates.

It also reduces the effect of geometric difference between

mages.

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.

This will make the process lessdependent on image orientation.

Set template size proportional to the

information content in the template.A smaller template size is sufficient

when the template is highly detailed

For a detailed area

compare o w en covers a ra erhomogeneous area.

For a less detailed area

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- - At image level: Reduce the size of images,

find the correspondences, and determinethe transformation parameters. Use thetransformation to resam le the ima es atone level higher resolution. Repeat theprocess until images at the highest

resolution are re istered.

At template level: Either use smallertemplates or cheaper similarity measures to

.the best match position from among thecandidates using a larger template and/or a

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.


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ur ng searc : Use arge steps to finpossible match positions. Then use finer

steps in the neighborhood of the likely

matches to refine the final match position.

Use partial information: If a large set of

an mar s s g ven, rs use a su se o

the landmarks to find approximate

registration parameters and then verify thecorrectness of the registration and refine

the parameters using all landmarks.

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1. A. Goshtasby and G. C. Stockman, Point pattern matching using convex-hull edges,IEEE

, , , .

2. W. J. Rucklidge, Efficiently locating objects using the Hausdorff distance,Int'l J.

Computer Vision, 24(3):251270 (1997).3. G. Stockman, S. Kopstein, and S. Benett, Matching images to models for registration and

object detection via clustering,IEEE Trans. Pattern Analysis and Machine Intelligence,(3):229241 (1982).

4. J. L. Mundy and A. Zisserman, Geometric Invariance in Computer Vision, The MIT Press,Cambridge, MA (1992).

5. J. Kittler and J. Illingworth, Relaxation labeling algorithms - A review,Image and Vision, .

6. L. S. Shapiro and J. M. Brady, Feature-based correspondence: An eigenvector approach,Image and Vision Computing, 10(5): 283288, 1992.

7. A. Goshtasby, S. H. Gage, and J. F. Bartholic, A two-stage cross correlation approach totemplate matching,IEEE Transactions on Pattern Analysis and Machine Intelligence,

: .

8. D. Holtkamp and A. Goshtasby, Precision registration and mosaicking of multicameraimages,IEEE Trans. Geoscience and Remote Sensing, 47(10):34463455, 2009.

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