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Object Recognition Based on Shape Similarity. Longin Jan Latecki Computer and Information Sciences Dept. Temple Univ., [email protected] Collaborators: Zygmunt Pizlo, Psychological Sciences Dept., Purdue Univ., Nagesh Adluru, Suzan Köknar-Tezel, Rolf Lakaemper, Thomas Young, Temple Univ.,

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Object recognition based on shape similarity l.jpg

Object Recognition Based on Shape Similarity

Longin Jan Latecki

Computer and Information Sciences Dept. Temple Univ., [email protected]

Collaborators:

Zygmunt Pizlo, Psychological Sciences Dept., Purdue Univ.,

Nagesh Adluru, Suzan Köknar-Tezel,Rolf Lakaemper, Thomas Young, Temple Univ.,

Xiang Bai, Huazhong Univ. of Sci. & Tech. Wuhan, China


Slide2 l.jpg

Object Recognition Process:

Source:

2D image of a 3D object

Object Segmentation

Contour Extraction

Contour Cleaning, e.g., Evolution

Contour Segmentation

Matching: Correspondence of Visual Parts


Motivation l.jpg
Motivation

  • Once a significant visual part is recognized the whole recognition process is strongly constrained in possible top-down object models.

  • (H1)object recognition is preceded by, and based on recognition of visual parts.

  • (H2): contour extraction is driven by shape similarity to a known shape.




Object contours l.jpg
Object contours object).

  • Psychophysical and neurophysiological studies provide an abundance of evidence that contours of objects are extracted in early processing stages of human visual perception.

  • Contours play a central role in the Gestalt-theory.





Visual parts and shape similarity l.jpg
Visual parts and shape similarity (Singh and Hoffman 2001)

  • (H1)object recognition is preceded by, and based on shape recognition of visual parts.

  • (H2): contour extraction is driven by shape similarity to a known shape.becomes:

  • (H2) Contour extraction is based on grouping of contour parts to larger contour parts with grouping assignments driven by shape familiarity.


Contour detection is a difficult inverse problem l.jpg
Contour detection is a difficult inverse problem (Singh and Hoffman 2001)

  • A given image could be produced by infinitely many possible 3D scenes. In order to produce a unique, stable and accurate interpretation, the visual system must use a priori constraints (see Pizlo, 2001 for a review).

  • The solution is obtained by optimizing a cost function which consists of two general terms: 1. how close the solution is to the visual data 2. how well the constraints are satisfied


Partial shape similarity l.jpg
Partial shape similarity (Singh and Hoffman 2001)


Partial shape similarity13 l.jpg
Partial shape similarity (Singh and Hoffman 2001)

Given only a part (of a shape), find similar shapes

  • (1) length problem,

  • (2) scale problem,

  • (3) distortion problem

Query Shape

Target Shape

Target Shape


Partial shape similarity14 l.jpg
Partial Shape Similarity (Singh and Hoffman 2001)

  • We reduce partial shape similarity to subsequence matching:

  • This is done by computing a curvature like value at every contour point.

  • We do this for complete contours of known objects in our database

  • and for query contour parts extracted from edge images


Slide15 l.jpg

Subsequence Matching (shape similarity) (Singh and Hoffman 2001)

Database

contours

Query

contours


Motivation for subsequence matching l.jpg
Motivation for subsequence matching (Singh and Hoffman 2001)

The top (red) and bottom (blue) sequences represent parts of contours of two different but very similar bone shapes


Motivation 2 l.jpg
Motivation(2) (Singh and Hoffman 2001)

Example sequences:

a = {1, 2, 8, 6, 8}

b = {1, 2, 9, 15, 3, 5, 9}


Osb algorithm l.jpg
OSB Algorithm (Singh and Hoffman 2001)

  • Goal: given two real-valued sequences a and b, find subsequences a’ of a and b’ of b such that a’ best matches b’

    • Possible to skip elements in both a and b

      • The ability to exclude outliers

    • Preserve the order of the elements

    • A one-to-one correspondence


Osb algorithm 2 l.jpg
OSB Algorithm (2) (Singh and Hoffman 2001)

  • Create a dissimilarity matrix

    • No restrictions on the distance function d

      • We used d(ai,bj) = (ai – bj)2

  • To find the optimal correspondence, use a shortest path algorithm on a DAG


Osb algorithm 3 l.jpg
OSB Algorithm (3) (Singh and Hoffman 2001)

  • The nodes of the DAG are all the index pairs of the matrix: (i,j){1,…,m}{1,…,n}

  • The edge weights w are defined by

    • C is the jump cost (the penalty for skipping an element)


Osb algorithm 4 l.jpg
OSB Algorithm (4) (Singh and Hoffman 2001)

  • The edge cost may be extended to impose a warping window

    • Set a maximal value for k – i – 1 and l – j - 1

  • This definition of the edge weights is our main contribution


A simple example l.jpg
A Simple Example (Singh and Hoffman 2001)

a = {1, 2, 8, 6, 8}

b = {1, 2, 9, 15, 3, 5, 9}

The dissimilarity matrix

d(ai,bj) = (ai – bj)2


Slide23 l.jpg

Key (Singh and Hoffman 2001)

(indices)

elements

distance

(1,1)

1 - 1

0

(1,2)

1 - 2

1

(1,3)

1 - 9

64

(1,4)

1 - 15

196

(1,5)

1 - 3

4

(1,6)

1 - 5

16

(1,7)

1 - 9

64

(2,1)

2 - 1

1

(2,2)

2 - 2

0

(2,3)

2 - 9

49

(2,4)

2 - 15

169

(2,5)

2 - 3

1

(2,6)

2 - 5

9

(2,7)

2 - 9

49

.

.

.

...

...

...

(3,1)

8 - 1

49

(3,2)

8 - 2

36

(3,3)

8 - 9

1

(3,4)

8 - 15

49

(3,5)

8 - 3

25

(3,6)

8 - 5

9

(3,7)

8 - 9

1

.

.

.

.

.

.

.

.

.

(4,1)

6 - 1

25

(4,2)

6 - 2

16

(4,3)

6 - 9

9

(4,4)

6 - 15

81

(4,5)

6 - 3

9

(4,6)

6 - 5

1

(4,7)

6 - 9

9

.

.

.

(5,1)

8 - 1

49

(5,2)

8 - 2

36

(5,3)

8 - 9

1

(5,4)

8 - 15

49

(5,5)

8 - 3

25

(5,6)

8 - 5

9

(5,7)

8 - 9

1

The DAG


Slide24 l.jpg

Experimental results on (Singh and Hoffman 2001)

MPEG 7 dataset,

1400 targets in 70 classes


Slide25 l.jpg

How to find contour parts in images (Singh and Hoffman 2001)?

  • Humans group contours automatically

  • An adaptive, probabilistic process to perform grouping

  • All shapes contain local symmetry  exploit local symmetry


Shape model l.jpg
Shape model (Singh and Hoffman 2001)


Play movie l.jpg
Play (Singh and Hoffman 2001)movie


Slide30 l.jpg

Contour Grouping (Singh and Hoffman 2001)as Robot Mapping

  • Rao-Blackwellized particle filter is an adaptive, probabilistic approach

  • Frequently utilized in SLAM approaches to Robot Mapping

  • Each particle’s successor is its most likely successor

  • Particles are resampled to eliminate poorly performing particles



Center points l.jpg
Center Points (Singh and Hoffman 2001)

  • Center points act as center points for maximal radius disk between the two sample points

  • Full set of center points gives full set of maximal radius disks

    • Entire set of potential skeletal points

    • Want to generate a skeletal path that best groups the segments for a given shape model


Center points and particle paths l.jpg
Center points and particle paths (Singh and Hoffman 2001)


Shape model34 l.jpg
Shape model (Singh and Hoffman 2001)

  • System needs to utilize reference model

    • Some a priori knowledge to discover the proper shape

    • Model is a sequence of radii at sample skeleton points

    • Position in reference model determined by triangulation


Contour smoothness l.jpg
Contour Smoothness (Singh and Hoffman 2001)

  • Smoothness as a criterion for segment selection

    • Smoothness is the measure of the amount of turn and the distance between segments

    • Use least sum of distance to determine both distance and the segment pairing

    • Smoothness as Gaussian mixture of distance and angle


Slam framework l.jpg
SLAM framework (Singh and Hoffman 2001)

  • Obtain particles by sampling from the maximum posterior probability

    • x is the path traversal

    • m is the contour grouping model

    • z is the observations

    • u is the reference model


Particle filter l.jpg
Particle filter (Singh and Hoffman 2001)

  • Sampling: The next generation of particles x(i)t is obtained from

  • the current generation x(i)t-1 by sampling from a proposal distribution

for


Slide38 l.jpg


Slide39 l.jpg

log(M(c (Singh and Hoffman 2001)2)) – log of pdf that a given pixel is a center point of radius 10


Slide40 l.jpg

log(M(c (Singh and Hoffman 2001)2)) – log of pdf that a given pixel is a center point of radius 10


Slide41 l.jpg

3) Resampling: Particles with a low importance weight w (Singh and Hoffman 2001)(i)

are typically replaced by samples with a high weight.

Residual resampling was used

4) Contour Estimating: For each pose sample x(i)t, the corresponding

contour estimate m(i)t is computed based on the trajectory

and the history of observations according to


Results l.jpg
Results (Singh and Hoffman 2001)

  • Grouping performed on several pictures

  • Useful groupings on many images

    • Little or no noise grouped

    • Few structural particles missed


Future work l.jpg
Future Work (Singh and Hoffman 2001)

  • Integration of the shape similarity of parts and the contour grouping

  • Learning good contour parts

  • Further improvements to the contour grouping to make it more robust


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