In its most widespread imaging and vision applications, Ambrosio and Tortorelli (AT) phase
field is a technical device for applying gradient descent to Mumford and Shah simultaneous …

Disk shape frequently appears as a reference in shape characterization applications. We
propose a local measure of deviation from a disk as the local difference between numerical …

From art to science, ornaments constructed by repeating a base motif (tiling) have been a
part of human culture. These ornaments exhibit various kinds of symmetries depending on …

Perception research provides strong evidence in favor of part based representation of
shapes in human visual system. Despite considerable differences among different theories …

Interesting phenomena in shape perception is nonlocal and nonlinear. Thus, it is crucial that
a shape perception system exhibits a nonlocal and nonlinear behaviour. From the …

Planar ornaments, aka wallpapers, are regular repetitive patterns which exhibit translational
symmetry in two independent directions. There are exactly 17 distinct planar symmetry …

The morphological skeleton transform (MST) is a leading morphological shape
representation scheme. In the MST, a given shape is represented as the union of all the …

We demonstrate the possibility of coding parts, features that are higher level than
boundaries, using a modified AT field after augmenting the interaction term of the AT energy …

We propose a variational approach to unsupervised texture segmentation that depends on
very few parameters and is robust to imaging conditions. First, the uneven illumination in the …

Extracting skeletons of 2D and 3D shapes is important for obtaining a compact
representation of shapes, which later can be utilized in various areas such as shape …