Practical reliable Bayesian recognition of 2D and 3D objects usingimplicit polynomials and algebraic invariants

We treat the use of more complex higher degree polynomial curves and surfaces of degree higher than 2, which have many desirable properties for object recognition and position estimation, and attack the instability problem arising in their use with partial and noisy data. The scenario discussed in this paper is one where we have a set of objects that are modeled as implicit polynomial functions, or a set of representations of classes of objects with each object in a class modeled as an implicit polynomial function, stored in the database. Then, given partial data from one of the objects, we want to recognize the object (or the object class) or collect more data in order to get better parameter estimates for more reliable recognition. Two problems arising in this scenario are discussed: 1) the problem of recognizing these polynomials by comparing them in terms of their coefficients; and 2) the problem of where to collect data so as to improve the parameter estimates as quickly as possible. We use an asymptotic Bayesian approximation for solving the two problems. The intrinsic dimensionality of polynomials and the use of the Mahalanobis distance are discussed     

Confidence modeling for handwriting recognition: algorithms and applications

Confidence scoring can assist in determining how to use imperfect handwriting-recognition output. We explore a confidence-scoring framework for post-processing recognition for two purposes: deciding when to reject the recognizer's output, and detecting when to change recognition parameters e.g., to relax a word-set constraint. Varied confidence scores, including likelihood ratios and posterior probabilities, are applied to an Hidden-Markov-Model (HMM) based on-line recognizer. Receiver-operating characteristic curves reveal that we successfully reject 90% of word recognition errors while rejecting only 33% of correctly-recognized words. For isolated digit recognition, we achieve 90% correct rejection while limiting false rejection to 13%.     

Describing complicated objects by implicit polynomials

This paper introduces and focuses on two problems. First is the representation power of closed implicit polynomials of modest degree for curves in 2-D images and surfaces in 3-D range data. Super quadrics are a small subset of object boundaries that are well fitted by these polynomials. The second problem is the stable computationally efficient fitting of noisy data by closed implicit polynomial curves and surfaces. The attractive features of these polynomials for Vision is discussed