Grey Weighted Polar Distance Transform for Outlining Circular and Approximately Circular Objects

Abstract

We introduce the polar distance transform and the grey weighted polar distance transform for computation of minimum cost paths preferring circular shape, as well as give algorithms for implementations in a digital setting. An alternative to the polar distance transform is to transform the image to polar coordinates, and then apply a Cartesian distance transform. By using the polar distance transform, resampling of the image and interpolation of new pixel values are avoided. We also handle the case of grey weighted distance transform in a 5 × 5 neighbourhood, which, to our knowledge, is new. Initial results of using the grey weighted polar distance transform to outline annual rings in images of log end faces are presented.

Spatially-variant morphological operations on binary images based on the polar distance transform

“…The polar distance transform [6], is a DT where the distance between two pixels is related to the pixels spatial relation to each other, as well as to an image origin. The origin is the (approximate) centre of a circular pattern and can be set by the user.…”

“…By assigning different weights to the radial and angular directions, respectively, and weighting the radial step higher, the PDT defines steps in the angular direction shorter than in the radial. To provide that the PDT is a metric, we use slightly different definitions of the weights, compared to [6]. 1 978-1-4244-2175-6/08/$25.00 ©2008 IEEE Definition 2.1.…”

“…We use the polar distance transform (PDT) presented in [6], where the distance between pixels depend on the polar coordinates. The PDT defines distance in angular direction different than distance in the radial direction, giving "discs" that are elongated either in the angular or in the radial direction.…”

An Optimal Choice of Morphological Operating Center for Object Image Retrieval

“…It has more advantages than the traditional Cartesian representation when processing and analyzing images which contain some kind of radial symmetry, or in general, which have "a center". Morphological image operators are usually designed on a trial and error basis by composing several simpler operators, each one with an appropriate SE [7]- [9]. Applying mathematical morphology to image distributed on the unit circle is not immediately possible [10], [11], as the unit circle is not a lattice.…”

An Automatic Method for Counting Annual Rings in Noisy Sawmill Images

“…The number of annual rings in region P D can be estimated by applying the greyweighted polar distance transform (GWPDT) described in [13]. The GWPDT is an anisotropic distance transform where the polar coordinates (r, θ) of the pixels are considered.…”