Symmetry Sensitivities of Derivative-of-Gaussian Filters

Abstract

We consider the measurement of image structure using linear filters, in particular derivative-of-Gaussian (DtG) filters, which are an important model of V1 simple cells and widely used in computer vision, and whether such measurements can determine local image symmetry. We show that even a single linear filter can be sensitive to a symmetry, in the sense that specific responses of the filter can rule it out. We state and prove a necessary and sufficient, readily computable, criterion for filter symmetry-sensitivity. We use it to show that the six filters in a second order DtG family have patterns of joint sensitivity which are distinct for 12 different classes of symmetry. This rich symmetry-sensitivity adds to the properties that make DtG filters well-suited for probing local image structure, and provides a set of landmark responses suitable to be the foundation of a nonarbitrary system of feature categories.

From BoW to CNN: Two Decades of Texture Representation for Texture Classification

“…It therefore shares the advantages of LBP over methods based on codebook learning with clustering. In contrast with LBP, BIF probes an image locally using Gaussian derivative filters [73,72] whereas LBP computes the differences between a pixel and its neighbors. Derivative of Gaussians (DtG), consisting of first and second order derivatives of the Gaussian filter, can effectively detect the local basic and symmetry structure of an image, and allows achieving exact rotation invariance [61].…”

Automated Texture Recognition of Quartz Sand Grains for Forensic Applications*

“…For both problems, images were encoded using BIFs (20,21), a system that assigns each location in an image to one of seven classes according to local symmetry type. The algorithm, which is given below, uses a bank of six derivative‐of‐Gaussian filters to assign the type as either light line on dark , dark line on light , light rotational, dark rotational , slope , saddle‐like , or flat .…”

“…Despite recent advances in texture recognition systems (15–19), there are no recorded instances of these systems being applied to forensic grain or particle analyses. Basic Image Features (BIFs) (20,21) have been used to provide excellent results for texture recognition when using standard texture data sets in the field of computer vision (16), and this paper presents the first application of this technique to QGSTA for forensic use. Therefore, the system presented here utilizes a well‐established method in Computer Vision to compute a BIF‐based texture description of the surface feature (for an example, see Fig.…”

Texture feature column scheme for single‐ and multi‐script writer identification

“…The oBIFs represent an extension to the Basic Image Features (BIFs) [42,43]. The key idea is to label each location in the image with one of the seven local symmetry classes.…”