亀田 裕介

Recently, a technique of visual cryptography which reveals a secret image by overlaying two other images has attracted attention. As an application of this technique, we propose a method to embed given QR codes in halftone images which can be recognized as the same natural image.

変分法に基づくオプテイカルフロー計算は，オプテイカルフローの条件から成る最小化問題の解として見かけの速度場を求める手法である．単純な画像列には，その動きを多義的に解釈できる場合が存在する．本論文では，動きの多義解釈について，変分法に基づくオプティカルフロー計算法の観点から考察し，オプティカルフローの条件式と境界条件を変えることによって動きの多義解釈が－部説明可能であること示す．数値実験では，各条件の元で計算されたオプテイカルフローが多義解釈の一部に相当することを示している．本研究により，これまで心理実験によって説明されてきた動きの多義解釈を数理的に説明できることを示す．Most of the methods to compute optical flows are variational-technique-based methods, which estimate appearance velocity fields by solving an energy minimization problem conposed of some conditions of the velocity fields. For simple images, sometimes the appearance motions of the images can be recognized ambiguously. In this paper, we discuss about the ambiguity of appearance motions form the viewpoint of the variational-technique-based method and show that the ambiguity is partially explicable by the theory of the method. Numerical experiments show that the optical flows computed under each condition correspond to the some of the ambiguity. Prom the results, we show that the theory of the variational-technique-based method can explain mathematically the ambiguities which have been represented by psycholigy experiments in the past.

オプテイカルフロー計算法の多くは変分法に基づく手法であり，画像関数が時空間的連続性を持つことと見かけの動きが小さいことを仮定している．時空間微分の離散化誤差の観点において，微分の差分近似精度の問題があるため，オプテイカルフローの適切な解像度は画像の解像度とフレームレートに依存する．つまり，低フレームレート画像の場合，オプティカルフローの適切な解像度は画像の解像度よりも小さくなるはずである．しかし，多くの従来手法はオプテイカルフローを画像と同じ解像度で求めている．したがって，解像度が高すぎる場合，画像のダウンサンプリングは変分法に基づく手法に対して有効に働く．本論文では，オプテイカルフローの誤差解析の観点から，変分法に基づく手法を用いたオプティカルフロー推定の適切な解像度について解析する．適切な解像度を推定するために，画像の解像度から構築した階層的構造を用いる．数値計算結果は低フレームレート画像の解像度を下げることが変分法に基づくオプテイカルフロー計算において有効であることを示している．Most of the methods to compute optical flows are variational-technique based methods, which assume that image functions have spatiotemporal continuities and also the appearance motions are small. In the viewpoint of the discrete errors of spatial- and time-differentials, the appropriate resolution of optical flow depends on both the resolution and frame rate of images since there is a problem about the accuracy of the discrete approximations of derivatives. Therefore, in the case of low frame-rate images, the appropriate resolution of optical flow should be lower than the resolution of images. However, many traditional methods estimate optical flow with same resolution of the images. Therefore, if the resolution is too high, down-sampling the images is effective to variational-technique based methods. In this paper, we analyze the appropriate resolutions of optical flows estimated by variational optical-flow computations from the viewpoint of the error analysis of optical flows. To analyze appropriate resolutions, we use hierarchical structures constructed from the multi-resolutions of images. Numerical results show that decreasing image resolutions is effective to compute optical flows by vaxiational optical-flow computations in low frame-rate sequences.

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.