Object Recognition Based on Shape Similarity Longin Jan Latecki Computer and Information Sciences Dept. Temple Univ., latecki@temple.edulatecki@temple.edu.
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Object Recognition Based on Shape Similarity
Longin Jan LateckiComputer and Information Sciences Dept. Temple
Univ., latecki@temple.eduCollaborators:
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
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Object Recognition Process:
Source:2D image of a 3D object
Matching: Correspondence of Visual Parts
Contour Segmentation
Contour Extraction
Object Segmentation
Contour Cleaning, e.g., Evolution
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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.
4What do you see?
5With grouping constraints we can see (i.e., recognize the object).
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Object contours 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.
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Salient visual parts can influence the object
recognition (Singh and Hoffman 2001)
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Salient visual parts can influence the object
recognition (Singh and Hoffman 2001)
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Salient visual parts can influence the object
recognition (Singh and Hoffman 2001)
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Visual parts and shape similarity (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.
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Contour detection is a difficult inverse problem
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
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Partial shape similarity
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Partial shape similarity (1) length problem, (2) scale problem, (3) distortion problem
Query Shape Target Shape Target Shape
Given only a part (of a shape ), find similar shapes
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Partial Shape Similarity 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
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Subsequence Matching (shape similarity)
Databasecontours
Querycontours
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Motivation for subsequence matching
OSB DTW
LCSS with threshold 0.50 LCSS with threshold 1.00
The top (red) and bottom (blue) sequences represent parts of contours of two different but very similar bone shapes
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Motivation(2)Example sequences:a = {1, 2, 8, 6, 8}b = {1, 2, 9, 15, 3, 5, 9}
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OSB Algorithm 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
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OSB Algorithm (2)
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
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OSB Algorithm (3)
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)
otherwise
if ),()2()1()),(),,((
22 ljkibadCjliklkjiw lk
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OSB Algorithm (4) 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
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A Simple Examplea = {1, 2, 8, 6, 8}b = {1, 2, 9, 15, 3, 5, 9}
b
1 2 9 15 3 5 9
a
1 0 1 64 196 4 16 64
2 1 0 49 169 1 9 49
8 49 36 1 49 25 9 1
6 25 16 9 81 9 1 9
8 49 36 1 49 25 9 1
d(ai,bj) = (ai – bj)2
The
dis
sim
ilarit
y m
atrix
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(indices)elementsdistance
Key
(1,1)1 - 1
0
(1,2)1 - 2
1
(1,3)1 - 964
(1,4)1 - 15196
(1,5)1 - 3
4
(1,6)1 - 516
(1,7)1 - 964
(2,1)2 - 1
1
(2,2)2 - 2
0
(2,3)2 - 949
(2,4)2 - 15169
(2,5)2 - 3
1
(2,6)2 - 5
9
(2,7)2 - 949
(3,1)8 - 149
(3,2)8 - 236
(3,3)8 - 9
1
(3,4)8 - 15
49
(3,5)8 - 325
(3,6)8 - 5
9
(3,7)8 - 9
1
(4,1)6 - 125
(4,2)6 - 216
(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 - 149
(5,2)8 - 236
(5,3)8 - 9
1
(5,4)8 - 15
49
(5,5)8 - 325
(5,6)8 - 5
9
(5,7)8 - 9
1
. . .
. . .. . .
. . .
. . .
... ......
The
DA
G
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Experimental results onMPEG 7 dataset,1400 targets in 70 classes
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Humans group contours automatically An adaptive, probabilistic process to
perform grouping All shapes contain local symmetry
exploit local symmetry
How to find contour parts in images?
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Shape model
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Play movie
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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
Contour Grouping as Robot Mapping
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Traversal space generated as discrete “center points”
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Center Points
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
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Center points and particle paths
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Shape model
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
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Contour Smoothness
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
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SLAM framework
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
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Particle filter
1) 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
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2) Importance Weighting: An individual importance weight w(i) is assigned to each particle, according to
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log(M(c2)) – log of pdf that a given pixel is a center point of radius 10
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log(M(c2)) – log of pdf that a given pixel is a center point of radius 10
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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
3) Resampling: Particles with a low importance weight w(i)
are typically replaced by samples with a high weight.Residual resampling was used
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Results Grouping performed on several
pictures
Useful groupings on many images Little or no noise grouped Few structural particles missed
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Future Work 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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