亀田 裕介

We introduce variational optical flow computation involving the prior with the fractional order differentiations. The fractional order differentiation is a typical tool in signal processing and image analysis. The zero crossing of a fractional order Laplacian yields a good performance for edge detection. As a sequel of edge detection with the fractional order differentiations, we deal with variational optical flow computation involving the fractional order differentiations on optical flow vectors. The method allows us to detect discontinuity of optical flow using linear operations.

本論文では、高次微分拘束を利用した変分法によるオプティカルフロー計算を提案し、拘束の次数によって画面上点の動きを分類できることを示す。オプティカルフローはベクトル場であるため、勾配法によるオプティカルフロー計算に、ベクトルスプライン拘束を採用することが行われる。また、変形体の境界壁の動きの抽出には、変形体の力学的性質から薄板スプライン拘束を利用することも行われる。１次ベクトルスプライン拘束は、Horn-Schunck 式に等価になる場合が知られている。また、２次ベクトルスプライン拘束が薄板スプラインと等価になる場合が知られている。そこで本論文では、微分拘束の次数の違いと、支配される物理現象の違いとを利用して違いを利用して、画面中の点の動きを分類する。In variational methods, a problem in computer vision and image analysis is expressed the sumation of the data-term and the prior-term. The data-term is usually constructed form observed data. The prior-term defined by knowledges and assumptions on the problem acts as regulariser to the data-term of the problem. A typical class of prior-terms defines smoothness of the solution. In this paper, we deal with energy functional with the higher order derivatives for vector valued functions and show that it is possible to classify the motions in an image using variational optical-flow computation. We classify the motions of points in an image using the priors with various order differential-constraints.Using the first and second order derivatives, we show that variational method with the first order constraints accurately extracts optical-flow vectors in texture areas and that variational method with the second order derivatives derives the motion of segment-boundaries. Therefore, the results shows that it is possible to classify the texture regions and segment-boundaries in an image using the first and second derivatives as the constraints of optical-flow computation.