The Application of the 2D Structure Tensor in Visual Arts and Design

Abstract

Tensors are a natural extension of matrices and vectors. They provide an ideal framework for abstracting relationships between related parameters. In image processing, tensors can be used to represent gradient information. The 2D structure tensor is one such representation, useful in corner detection and non- photorealistic rendering. This abstract summarizes my image processing filter based on the 2D structure tensor that generates artistic abstraction from photographs. With the 2D structure tensor, I explored ways to present the gradient directions of an image as artwork and investigated the relationship between the Gabor filter and the eigenvectors of the 2D structure tensor. Using this filter, I produce images that consist of a dense patchwork of lines, somewhat resembling certain artistic types of pen shading such as hatching and cross-contour shading. By applying this filter, I have found ways to categorize images that display salient groups of parallel lines. These images present a higher artistic quality and display better compositional style after being processed using the 2D structure tensor than the average photograph. Another finding is that not all resolutions of images are ideal for structure tensor processing and that an image size of 700-1000 pixels per side yields the best results from both a mathematical and artistic standpoint.