類似度関数を用いた確率的緩和法
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概要
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パターン認識過程は、入力パターンの帰属するであろう候補カテゴリ候補を単一の元から成る候補カテゴリに絞っていくものである[3],[4]。 本論文では、1つのパターンφについての認識の働きを万能的に備えている認識システムRECOGNITRONの研究[3],[4]とは異なり、1つの画面内に、n個の物体像φ₁,φ₂,…,φn∈Φ⊂ℌがあると判明したとき、各物体φk(k=1～n)に、m個のカテゴリℭ₁,ℭ₂,…,ℭmの内、如何なるカテゴリを付与すべきかが、両立性の程度CM(φk,φe;ℭi,ℭj)と影響の程度IF(φk,φe)が新しく一般抽象ヒルベルト空間ℌ(⊃Φ)上で導入され(2例1.1,1.2)、類似度関数[3],[4]SMを初期条件とする更新アルゴリズム(2.2.2項)を採用するSM確率的ラベリング弛緩法が収束するための諸条件が厳密かつ詳細に研究されている。 Let us suppose that a process of recognizing a pattern is to narrow down a set of categories to which the pattern may possibly belong and to convert the set to a set which contains only an element [3], [4]. In this paper, instead of dealing with a recognition system RECOGNITRON [3], [4] which can possess of an universal faculty of recognition only for any pattern in question, we shall research which category of m categories ℭ₁, ℭ₂, …, ℭm each of n objects (patterns) φ₁,φ₂, …, φn ∈Φ⊂ℌ (a Hilbert space) should be simustaneously assigned. Using compatibility measure CM (φk,φe; ℭi, ℭj) of pattern φk having category ℭi when pattern φe having ℭj and influence coefficient IF(φk,φe) of pattern φk from pattern φe, a new probabilistic relaxation labeling method with regard to similarity measure SM defined in appendix A is proposed based on literature [39], where quantity SM (φk,ωi; t) is the probability of the k-th pattern φk having the i-th category ℭi at step t. The dynamics of the relaxation system and the relationship between convergence properties and system parameters are studied analytically and strictly in detail.
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