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UCSD CSE 252C - Face Recognition Using a Line Edge Map

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Face Recognition Using a Line Edge MapYongsheng Gao and Maylor K.H. Leung at Nanyang Tech. UniversityIEEE Pattern Analysis and Machine Intelligence 2002Slides by David Anthony TorresComputer Science and Engineering — University of California at San DiegoInterest 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 infoLine 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 matchingLine 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 I1and I2.Hausdorff Distance• i and j are edge pixel positions (x,y).• For each pixel i in I1Find 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.211211(, ) min || ||||jIiIhI I i jI∈∈=−∑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 mapLine Edge Map• LEM is a series of line segments.! LEM records only the endpoints of lines.! Further reduces storage requirements.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.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 segmentsLine-Segment Hausdorff Distancesmallest intersecting angleLine-Segment Hausdorff Distance• f() is a penalty function: f(θ) = θ2/W! Higher penalty on large deviation• W is determined in training.Line-Segment Hausdorff DistanceminLine-Segment Hausdorff Distance•In general lines will not be parallel•So rotate the shortest lineLine-Segment Hausdorff Distance• Finally,• Primary line-segment Hausdorff Distance (LHD)(, ) max((, ), ( ,))HIJ hIJ hJI=where1(, ) || ||min (, )|| ||jJiIiIhI J i di ji∈∈∈=⋅∑∑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.Neighborhoods• Positional neighborhood Np• Angular neighborhood Na• Heuristic: lines that fall within the neighborhood are probably matches.Θ-neighborhoodLine Segment in IMatching Line-segmentin JNeighborhoods•If ≥1 line falls into the neighborhoods we call the original line segment I, a high confidence line.Θ-neighborhoodLine Segment in Iis a High Confidence LineMatching Line-segmentin JHigh Confidence Ratio• Nhcis the num. of high confidence lines in a LEM.• Ntotalis the total num. of lines in a LEM.InputModelNew Hausdorff Distance•Wnis a weight. •Dnis the average number of lines (across input and model) that are not confidently-matched, i.e.22'( , ) ( , ) ( )nnHTM H TM WD=+RTand RMare the high confidence ratios for input and model respectivelySummary• Start with to LEM’s• Calculate Hausdorff DistanceInputModel(, ) max((, ), ( ,))HIJ hIJ hJI=1(, ) || ||min (, )|| ||jJiIiIhI J i di ji∈∈∈=⋅∑∑Summary••Summary• Finally we take into account the effect of neighborhoods •22'( , ) ( , ) ( )nnHTM H TM WD=+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 22'( , ) ( , ) ( )nnHTM H TM WD=+ResultsFace Recognition under Controlled ConditionsBern DatabaseAR DatabaseFace Recognition under Controlled ConditionsFace Recognition under Controlled ConditionsFace Recognition under Controlled Conditionsw/o neighborhood heuristicSensitivity to Size Variation• Used the AR data base.• Applied a random scaling factor of ±10%Recognition Under Varying LightingRecognition Under Facial Expression ChangesView Based Identification — “Leave One Out” Experiment.Recognition Under Varying PoseAdditional Material…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.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.Face Pre-filteringFace Pre-filteringFace Pre-filteringFace Pre-filteringFace Pre-filteringFace Pre-filteringFace Pre-filteringFace -PrefilteringNow for some hand-waving action... • Rotate the Gaussian so that its axis aligned• Perform a change of coordinates into a polar system••To summarize• Given a probability F(d) we can obtain a constant density ellipse of the form:•whereTo summarize• So if the error vector satisfies:• then the model is classified as a potential face.Pre-Filtering Results• Train to find parameter above.• Small rho indicates vector components are nearly


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