face recognition using a line edge map · Ł takÆcs (1998) used edge maps for face...
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Face Recognition Using a Line Edge Map
Yongsheng Gao and Maylor K.H. Leung at Nanyang Tech. University
IEEE Pattern Analysis and Machine Intelligence 2002
Slides by David Anthony TorresComputer Science and Engineering — University of California at San Diego
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Interest Points Vs. Edge Maps
� Interest point detectors are popular!SIFT, Harris/Forstner
� What about edge information?!Can carry distinguishing info too.! Interest points don’t capture this info
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Line Edge Map
� Humans recognize line drawings well.!Maybe computer algorithms can too.
� Benefits of using edge information:!Advantages of template matching and geometrical
feature matching:" Partially illumination-invariant" Low memory requirement" Recognition performance of template matching
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Line Edge Map
� Takács (1998) used edge maps for face recognition.!Apply edge-detector to get a binary input image I! I is a set of edge points.!Use Hausdorff distance to measure the similarity
between two sets of points I1 and I2.
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Hausdorff Distance
� i and j are edge pixel positions (x,y).� For each pixel i in I1
Find the closest corresponding pixel j in I2Take the average of all these distances ||i-j||.
� Calculated without explicitly pairing the sets of points.
� Achieved a 92% accuracy in their experiments.
211 2
1
1( , ) min || ||| | j Ii I
h I I i jI ∈∈
= −∑
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Line Edge Map
� Takács Edge Map doesn�t consider local structure.
� Authors introduce the Line Edge Map (LEM)
� Groups edge pixels into line segments.!Apply polygonal line fitting to a
thinned edge map
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Line Edge Map
� LEM is a series of line segments.!LEM records only the endpoints
of lines.!Further reduces storage
requirements.
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Line-Segment Hausdorff Distance (LHD)� Need a new distance measure between sets of
line segments.� Expect it to be better because it uses line-
orientation. � First we�ll see an initial model�� Add to the model to make it more robust
!Encourage one-one mapping of lines!Encourage mapping of “similar” lines.
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Line-Segment Hausdorff Distance
� Given two LEMs S=(s1,s2,�sp) and T=(t1,t2,�sq)� The LHD is built on the vector d(si,tj)
!d() represents the distance between two lines segments
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Line-Segment Hausdorff Distance
smallest intersecting angle
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Line-Segment Hausdorff Distance
� f() is a penalty function: f(θ) = θ2/W!Higher penalty on large deviation
� W is determined in training.
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Line-Segment Hausdorff Distance
min
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Line-Segment Hausdorff Distance
�In general lines will not be parallel�So rotate the shortest line
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Line-Segment Hausdorff Distance� Finally,
� Primary line-segment Hausdorff Distance (LHD)
( , ) max( ( , ), ( , ))H I J h I J h J I=where
1( , ) || || min ( , )|| || j Ji I
i I
h I J i d i ji ∈∈
∈
= ⋅∑∑
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Some Problems�
� Say T is an input LEM, M is its matching model LEM, and N is some other non-matching model.
� Due to segmentation problems it could be the case that
H(T,M) >> H(T,N)� Keeping track of matched line-pairs could
help.
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Neighborhoods
� Positional neighborhood Np
� Angular neighborhood Na
� Heuristic: lines that fall within the neighborhood are probably matches.
Θ-neighborhood
Line Segment in I
Matching Line-segmentin J
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Neighborhoods
� If ≥1 line falls into the neighborhoods we call the original line segment I, a high confidence line.
Θ-neighborhood
Line Segment in Iis a High Confidence Line
Matching Line-segmentin J
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High Confidence Ratio
� Nhc is the num. of high confidence lines in a LEM.
� Ntotal is the total num. of lines in a LEM.
Input Model
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New Hausdorff Distance
� Wn is a weight. � Dn is the average number of lines (across input and
model) that are not confidently-matched, i.e.
2 2'( , ) ( , ) ( )n nH T M H T M W D= +
RT and RM are the high confidence ratios for input and model respectively
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Summary
� Start with to LEM�s
� Calculate Hausdorff Distance
Input Model
( , ) max( ( , ), ( , ))H I J h I J h J I=
1( , ) || || min ( , )|| || j Ji I
i I
h I J i d i ji ∈∈
∈
= ⋅∑∑
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Summary
�
�
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Summary
� Finally we take into account the effect of neighborhoods
�
2 2'( , ) ( , ) ( )n nH T M H T M W D= +
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Free Parameters
� We have four free parameters to fix!(W, Wn, Np, Na)
" θ2/W = f(θ) = dθ"
"Neighborhoods Np, Na
� Use simulated annealing to estimate!With probability
2 2'( , ) ( , ) ( )n nH T M H T M W D= +
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Results
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Face Recognition under Controlled Conditions
Bern Database
AR Database
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Face Recognition under Controlled Conditions
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Face Recognition under Controlled Conditions
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Face Recognition under Controlled Conditions
w/o neighborhood heuristic
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Sensitivity to Size Variation
� Used the AR data base.� Applied a random scaling factor of ±10%
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Recognition Under Varying Lighting
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Recognition Under Facial Expression Changes
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View Based Identification � �Leave One Out� Experiment.
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Recognition Under Varying Pose
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Additional Material�
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Matching Time for LEM
� LEM takes longer than eigenface! Time O(Nn) > O(Nm)
" N is # of faces" n is avg. # LEM-features" m is # eigenvectors
� Authors propose a face pre-filtering scheme!Idea: filter out faces before performing
matching.
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Face Prefiltering
� Quantize an LEM into :
� Where Γ is the sum of line segment lengths
�
where υ is the angle if the angle is <90 degrees.
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Face Pre-filtering
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Face Pre-filtering
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Face Pre-filtering
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Face Pre-filtering
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Face Pre-filtering
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Face Pre-filtering
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Face Pre-filtering
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Face -Prefiltering
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Now for some hand-waving action... � Rotate the Gaussian so that its axis aligned� Perform a change of coordinates into a polar system
�
�
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To summarize
� Given a probability F(d) we can obtain a constant density ellipse of the form:
� where
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To summarize
� So if the error vector satisfies:
� then the model is classified as a potential face.
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Pre-Filtering Results
� Train to find parameter above.� Small rho indicates vector components are nearly independent.
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