A Bidirectional Matching Algorithm for Deformable Pattern Detection with Application to Handwritten Word Retrieval by K.W. Cheung, D.Y. Yeung, R.T. Chin {wiliam, dyyeung,

Model representation H j (Cubic B-spline) Model shape parameter w (Control pts.) parameter space w1w1 w2w2 w3w3 Hj(w3)Hj(w3) Hj(w2)Hj(w2) Hj(w1)Hj(w1) Modeling

Criterion Function Formulation Model Deformation Criterion Data Mismatch Criterion Mahalanobis distance Negative log of product of a mixture of Gaussians

Bayesian Formulation Prior distribution (without data) Likelihood function Posterior distribution (with data)

Bayesian Inference: Matching Matching by maximum a posteriori (MAP) estimation using the EM algorithm. parameter space MAP estimate

The Outlier Problem The mixture of Gaussians noise model fails when some gross errors (outliers) are present. Badly Segmented InputWell Segmented Input True data Outliers

Reverse Framework Model, H i (Uniform prior) Shape parameter, w (Prior distribution of w) Regularization parameter,  (Uniform prior) Data, D (Likelihood function of w) Stroke width parameter,  (Uniform prior) Multivariate Gaussian Mixture of Gaussians Direction of Generation From Model to Data

A Dual View of Generativity The Sub-part Problem The Outlier Problem

Forward Framework Model, H i Shape parameter, w Regularization parameter,  (Uniform prior) Data, D (Uniform prior) Model localization parameter,  (Uniform prior) Multivariate Gaussian Mixture of Gaussians (each data point is a Gaussian center) Direction of Generation From Data to Model

New Criterion Function Sub-data Mismatch Criterion Negative log of product of a mixture of Gaussians Old Data Mismatch Criterion

Forward Matching Matching –Optimal estimates {w *, A *, T *,  *,  * } are obtained by maximizing –Again, the EM algorithm is used. The old model parameter prior Model parameters generated by the data

Frameworks Comparison Outlier problem solved Sub-part problem solved

Bidirectional Matching Algorithm A matching algorithm is proposed which possesses the advantages of the two frameworks. The underlying idea is to try to obtain a correspondence between the model and data such that the model looks like the data AND vice versa (i.e., the data mismatch measures for the two frameworks should both be small.).

Bidirectional Matching Algorithm Initialization by Chamfer matching Forward Matching Compute the data mismatch measures for the two frameworks, E mis and E sub-mis Reverse Matching E mis > E sub-mis ?  :=(1+  )  if  :=4 Converge ? yes no

Experiment (I) Forward Matching Reverse Matching Bidirectional Matching

Experiment (I) * Results are obtained by visual checking. To extract leftmost chars. from handwritten words. Test Set - CEDAR database Model Initialization by Chamfer matching

Experiment (II) To retrieve handwritten words with its leftmost character similar to an input shape query. Test Set - CEDAR database –100 handwritten city name images Query Set

Experiment (II) Best N Approach Recall = 59% Precision = 43% # of candidates = 10

Experiment (II) Evidence Thresholding Recall = 65% Precision = 45% Averaged # of candidates = 12.7