Idempotent, direction-consistent anisotropic diffusion.

摘要

This thesis focuses on two of the most critical problems in the field of anisotropic diffusion (AD), viz. automatically stopping the diffusion process and selecting a suitable threshold for edges, that remained unsolved since AD theory was introduced in 1987 [171].; Over-smoothing of semantically meaningful features occurs very easily with Traditional AD (TAD) filters if the number of iterations is not carefully selected. Our research explains why TAD approaches do not act as might be expected from current AD theory. Idempotent AD (IAD), a new interpretation of AD using the non-negative part of the derivative of flux (DF) to control the smoothing strength, is proposed. A behavioral analysis is presented in detail of the AD process along the whole gradient magnitude due to the conduction function (CF). The analysis shows that a mathematically well-posed, a mathematically ill-posed or an idempotent diffusion process can be produced by the same CF. A criterion for selecting the CF is created. A threshold is proposed for true edges. We show the form of the discrete version of AD (DAD) whose solution converges to that of its continuous counterpart stably and consistently. Our proposed IAD keeps meaningful edges throughout the diffusion process with noise being smoothed, thereby making the experimental results agree with AD theory for the first time since 1987.; Choosing a suitable threshold is very important for AD techniques because it controls which edges are preserved. Determining this threshold with gradient-magnitude-based edge estimator (GMEE) is image dependent and becomes very complex with the appearance of noise and changes in illumination. This stubborn problem is avoided by the proposed idempotent, direction-consistent AD technique (IDCAD). This new technique uses a new criterion for implementing AD, combining the merits of a direction-consistency-based edge estimator (DCEE) and those of IAD. DCEE has low sensitivity to noise because regions containing edges show much more consistent edge directions as compared to regions of noise. Our algorithm implements IAD on noise regions located by DCEE.; Experiments carried out on 1D and 2D images with both artificial and real images validate the effectiveness of the proposed IAD and IDCAD techniques.