キーワード：方向検出、エッジ検出、テクスチャ解析、微分フィルタ、重ね合わせの原理、ハイパーコラム、ウエーブレット
Abstract This paper provides a computational framework for representing and detecting multiple orientation fields from a set of local differentiation filters such as multi-scale Gaussian derivatives. In contrast to the previous work on steerable filters by Freeman & Adelson, the representation is direct and closed-form, i.e., we do not need to steer the filters to detect multiple orientations, but can estimate them in a single-shot manner by solving algebraic equations. Further, the filter does not need to be strongly tuned to orientations, since the derived algorithm does not suffer from the problem of interference between signal components of the multiple orientations. The capability of extracting the characteristic image structures of different scales are demonstrated by simulations. These advantages are accomplished by using the Principle of Superposition. Our framework suggests a mathematical basis of efficient and compact multi-scale, multi-orientation image representation in the hypercolumn of primary visual cortex.
Keywords: Orientation detection, Edge detection, Texture analysis, Differentiation filters, Principle of Superposition, Hypercolumn, Wavelet