エドガルド クレグ,志沢雅彦
多価正則化ネットワーク
- 多重表面復元と2重運動検出への応用 -
Abstract:Feedforward neural networks are usually employed in the learning of an input-output mapping from a given (finite) set of sample data. When the mapping to be approximated is single-valued, these networks are known to successfully perform the approximation task without altering the composition of the learning data. However, for the case of multivalued functions, i.e. functions that assign multiple values to each point in the input space, it is necessary to cluster the data into groups that correspond to different hypersurfaces on the output space[3]. Such an additional task is computationally burdensome, especially with noisy learning data.
The approximation of multi-valued functions can be viewed as a mathematical framework that provides a solution to one of the problems encountered in computer vision, namely that of multiple transparencies, where it is necessary to reconstruct occluding surfaces (assumed to possess a certain degree of smoothness) from a given set of data[5][6].
Multi-Valued Regularization Networks (MVRN) have been proposed to solve this problem. MVRNs are derived from the Multi-Valued Standard Regularization theory (MVSRT), which is an extension of the standard regularization theory to multi-valued functions[1][3]. The idea is to represent the mapping by a single algebraic equation which is linear with respect to the coefficient functions. This representation then yields a linear Euler-Lagrange equation for the resulting energy minimization problem, thus facilitating the extension of the techniques used to derive regularization networks to the approximation of multi-valued functions.
A brief discussion of MVSRT and the derivation of MVRNs are given in the next section, while some numerical experiments that suggest the power of MVRNs in solving surface transparency problems in computational vision are described in the last section.