Prolongation in Good Continuation

Abstract

Smooth continuation of contours or lines also filling large gaps with illusory structure may be seen as the most stunning example for perceptual grouping. Much of the Gestalt literature on human seeing is about this topic. This must not be confused with the repetition of Gestalten in frieze symmetry. This chapter first presents a proven standard approach to this issue: the tensor voting. This technique is based on a smooth function on the 2D-domain similar to the assessments used elsewhere in this book. However, this function is matrix-valued, a field of symmetric positive semi-definite 2x2 matrices. In its classical use, this tensor field is rasterized and accumulated on the pixel grid, but this chapter shows ways to use the continuous field within the framework of this book. Tensor voting also generalizes well to higher dimensions, but that is beyond the scope of this book. Instead, the chapter also presents an operation for linear prolongation that fits well in the Gestalt-algebra approach and has proven useful in particular for the analysis of remotely sensed images of urban terrain.