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Object Detection Using Semi- Naïve Bayes to Model Sparse Structure Henry Schneiderman Robotics Institute Carnegie Mellon University

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Object Detection Find all instances of object X (e.g. X = human faces)

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Examples of Detected Objects

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Sparse Structure of Statistical Dependency Chosen variable

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Sparse Structure of Statistical Dependency Chosen coefficient

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Sparse Structure of Statistical Dependency Chosen coefficient

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Detection using a Classifier “Object is present” (at fixed size and alignment) “Object is NOT present” (at fixed size and alignment) Classifier

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Proposed Model: Semi-Naïve Bayes Kononenko (1991), Pazzini (1996), Domingos and Pazzini (1997), Rokach and Maimon (2001) e.g. S 1 = (x 21, x 34, x 65, x 73, x 123 ) S 2 = (x 3, x 8, x 17, x 65, x 73, x 111 ) subsets input variables

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Goal: Automatic subset grouping S 1 = (x 21, x 34, x 65, x 73, x 123 ) S 2 = (x 3, x 8, x 17, x 65, x 73, x 111 )... S n = (x 14, x 16, x 17, x 23, x 85, x 101, x 103, x 107 )

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Approach: Selection by Competition x 1 x 2 x 3... x m S 1 S 2... S q Generate q candidate subsets log [p 1 (S 1 | 1 ) / p 1 (S 1 | 2 )] log [p 2 (S 2 | 1 ) / p 2 (S 2 | 2 )]... log [p q (S q | 1 ) / p q (S q | 2 )] Train q log likelihood function Select combination of n candidates log [p j1 (S j1 | 1 ) / p j1 (S j1 | 2 )] log [p j2 (S j2 | 1 ) / p j2 (S j2 | 2 )]... log [p jn (S jn | 1 ) / p jn (S jn | 2 )] H(x 1,…,x r ) = log [p j1 (S j1 | 1 ) / p j1 (S j1 | 2 )]+log [p j2 (S j2 | 1 ) / p j2 (S j2 | 2 )] log [p jn (S jn | 1 ) / p jn (S jn | 2 )] q functions n functions, n << q

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Approach: Selection by Competition x 1 x 2 x 3... x m S 1 S 2... S q Generate q candidate subsets log [p 1 (S 1 | 1 ) / p 1 (S 1 | 2 )] log [p 2 (S 2 | 1 ) / p 2 (S 2 | 2 )]... log [p q (S q | 1 ) / p q (S q | 2 )] Train q log likelihood function Select combination of n candidates log [p j1 (S j1 | 1 ) / p j1 (S j1 | 2 )] log [p j2 (S j2 | 1 ) / p j2 (S j2 | 2 )]... log [p jn (S jn | 1 ) / p jn (S jn | 2 )] H(x 1,…,x r ) = log [p j1 (S j1 | 1 ) / p j1 (S j1 | 2 )]+log [p j2 (S j2 | 1 ) / p j2 (S j2 | 2 )] log [p jn (S jn | 1 ) / p jn (S jn | 2 )]

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Generation of Subsets “modeling error for assuming independence” q is size of the subset

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Generation of Subsets Selection of variables - “discrimination power” q is size of the subset

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Pair-Wise Measurement pair-wise measurements Pair-affinity

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Visualization of C(x,*) (frontal faces) x x x

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Measure over a Subset Subset-affinity

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Generation of Candidate Subsets x 1 x 2 x x m S 1 S S p Heuristic search and selective evaluation of D(S i ) C(x 1, x 2 ) C(x 1, x 3 ) C(x m-1, x m )

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subset size vs. modeling power Model complexity limited by number of training examples, etc. Examples of limited modeling power –5 modes in a mixture model –7 projection onto principal components

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Approach: Selection by Competition x 1 x 2 x 3... x m S 1 S 2... S q Generate q candidate subsets log [p 1 (S 1 | 1 ) / p 1 (S 1 | 2 )] log [p 2 (S 2 | 1 ) / p 2 (S 2 | 2 )]... log [p q (S q | 1 ) / p q (S q | 2 )] Train q log likelihood function Select combination of n candidates log [p j1 (S j1 | 1 ) / p j1 (S j1 | 2 )] log [p j2 (S j2 | 1 ) / p j2 (S j2 | 2 )]... log [p jn (S jn | 1 ) / p jn (S jn | 2 )] H(x 1,…,x r ) = log [p j1 (S j1 | 1 ) / p j1 (S j1 | 2 )]+log [p j2 (S j2 | 1 ) / p j2 (S j2 | 2 )] log [p jn (S jn | 1 ) / p jn (S jn | 2 )]

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Log-likelihood function = Table S i = (x i1, x i2,..., x iq ) vector quantization table look-up

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Sub-Classifier Training by Counting P i (f i | 1 ) P i (f i | 2 ) fifi fifi

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Example of VQ x i1 x i2 x i3... x iq c 1 c 2 c 3 z 1 z 2 z 3 f = z 1 m 0 + z 2 m 1 + z 3 m 2 quantization to m levels projection on to 3 principal components

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Approach: Selection by Competition x 1 x 2 x 3... x m S 1 S 2... S q Generate q candidate subsets log [p 1 (S 1 | 1 ) / p 1 (S 1 | 2 )] log [p 2 (S 2 | 1 ) / p 2 (S 2 | 2 )]... log [p q (S q | 1 ) / p q (S q | 2 )] Train q log likelihood function Select combination of n candidates log [p j1 (S j1 | 1 ) / p j1 (S j1 | 2 )] log [p j2 (S j2 | 1 ) / p j2 (S j2 | 2 )]... log [p jn (S jn | 1 ) / p jn (S jn | 2 )] H(x 1,…,x r ) = log [p j1 (S j1 | 1 ) / p j1 (S j1 | 2 )]+log [p j2 (S j2 | 1 ) / p j2 (S j2 | 2 )] log [p jn (S jn | 1 ) / p jn (S jn | 2 )]

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h 1 (S 1 ) h 2 (S 2 )... h P (S P ) E 1, 1 E 1, 2 E 2, 1 E 2, 2... E p, 1 E p, 2 Evaluate on training data ROC 1 ROC 2... ROC P Evaluate ROCs Order top Q log-likelihood functions h j1 (S j1 ) h j2 (S j2 )... h jQ (S jQ ) Candidate log-likelihood functions

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h j1 (S j1 ) + h 1 (S 1 )... h jQ (S jQ ) + h p (S p ) Form pQ pairs of log-likelihood functions E j1, 1 + E 1, 1 E j1, 2 + E 1, 2... E jQ, 1 + E p, 1 E jQ, 2 + E p, 2 Sum Evaluations ROC 1... ROC QP Evaluate ROCs Order top Q pairs of log-likelihood functions h k1,1 (S k1,1 ) + h k1,2 (S k1,2 )... h kQ,1 (S kQ,1 ) + h kQ,2 (S kQ,2 )... Repeat for n iterations

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H 1 (x 1, x 2,..., x r )... H Q (x 1, x 2,..., x r ) Cross-Validation Selects Classifier Q Candidates: H 1 (x 1, x 2,..., x r ) = h k1,1 (S k1,1 ) + h k1,2 (S k1,2 ) h k1,n (S k1,n )... H Q (x 1, x 2,..., x r ) = h kQ,1 (S kQ,1 ) + h kQ,2 (S kQ,2 ) h Q,n (S kQ,n ) H * (x 1, x 2,..., x r ) Cross-validation

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Example subsets learned for telephones

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Evaluation of Classifier “Object is present” (at fixed size and alignment) “Object is NOT present” (at fixed size and alignment) Classifier

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1) Compute feature values f 2 = #3214 f 1 = #5710 f n = #723

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2) Look-Up Log-Likelihoods P 1 ( #5710 | 1 ) P 1 ( #5710 | 2 ) f 2 = #3214 f 1 = #5710 f n = #723 = 0.53 P 2 ( #3214 | 1 ) P 2 ( #3214 | 2 ) = 0.03 log P n ( #723 | 1 ) P n ( #723 | 2 ) = 0.23 log

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3) Make Decision P 1 ( #5710 | 1 ) P 1 ( #5710 | 2 ) = 0.53 P 2 ( #3214 | 1 ) P 2 ( #3214 | 2 ) = 0.03 log P n ( #723 | 1 ) P n ( #723 | 2 ) = 0.23 log > <

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Detection using a Classifier “Object is present” (at fixed size and alignment) “Object is NOT present” (at fixed size and alignment) Classifier

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View-based Classifiers Face Classifier #1 Face Classifier #2 Face Classifier #3

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Detection: Apply Classifier Exhaustively Search in position Search in scale

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Decision can be made by partial evaluation P 1 ( #5710 | 1 ) P 1 ( #5710 | 2 ) = 0.53 P 2 ( #3214 | 1 ) P 2 ( #3214 | 2 ) = 0.03 log P n ( #723 | 1 ) P n ( #723 | 2 ) = 0.23 log > <

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Detection Computational Strategy Computational strategy changes with size of search space Apply log [p 1 (S 1 | 1 ) / p 1 (S 1 | 2 )] exhaustively to scaled input image Apply log [p 2 (S 2 | 1 ) / p 2 (S 2 | 2 )] reduced search space Apply log [p 3 (S 3 | 1 ) / p 3 (S 3 | 2 )] further reduced search space

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Repeat for N 2 Candidates Compute M 2 feature valuesLook-up M 2 log-likelihood values Candidate-Based Evaluation

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Repeat for N 2 Candidates Compute N 2 + M 2 +2MN feature valuesLook-up M 2 log-likelihood values Feature-Based Evaluation

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Create candidate subsets Train candidate log-likelihood functions Select log-likelihood functions Retrain selected log-likelihood functions using Adaboost Training images of object Cross-validation images Training images of non- object Determine detection threshold Automatically select non-object examples for next stage Images that do not contain object Increment stage Cascade Implementation Adaboost using confidence-rated predictions [Shapire and Singer, 1999] Bootstrapping [Sung and Poggio, 1995]

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Boosting... H(x 1, x 2,..., x r ) = h j1 (S j1 ) + h j2 (S j2 ) h jn (S jn ) x 1 x 2 x 3... x m S 1 S 2... S p Generate p candidate subsets; p >> n h 1 (S 1 ) h 2 (S 2 )... h p (S p ) Train p candidate sub-classifiers h j1 (S j1 ) h j2 (S j2 )... h jr (S jn ) Select combination of n candidates Retrain with Adaboost using confidence-rated predictions [Shapire and Singer, 1999]

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Face, eye, ear detection

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Frontal Face Detection Recognition rate85.2%89.7%92.1%93.7%94.2% False detections (this method) False Detections [Viola and Jones, CVPR, 2001] MIT-CMU Frontal Face Test Set [Sung and Poggio, 1995; Rowley, Baluja and Kanade, 1997] –180 ms 300x200 image –400 ms 300x500 image Top Rank Video TREC 2002 Face Detection Top Rank 2002 ARDA VACE Face Detection algorithm evaluation AMD Athalon 1.2GHz

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Face & Eye Detection for Red-Eye Removal from Consumer Photos CMU Face Detector

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Eye Detection Experiments performed independently at NIST Sequested data set: 29,627 mugshots Eyes correctly located (radius of 15 pixels) 98.2% (assumed one face per image) Thanks to Jonathon Phillips, Patrick Grother, and Sam Trahan for their assistance in running these experiments

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Realistic Facial Manipulation: Earring Example With Jason Pinto

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Telephone Detection

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Cart, pose 1

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Cart, pose 2

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Cart, pose 3

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Door Handle Detection

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Summary of Classifier Design Sparse structure of statistical dependency in many image classification problem Semi-naïve Bayes Model Automatic learning structure of semi-naïve Bayes classifier: –Generation of many candidate subsets –Competition among many log-likelihood functions to find best combination CMU on-line face detector:

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