A Fractal-Based Approach to Network Characterization Applied to Texture Analysis

Abstract

This work proposes a new method for texture analysis that combines fractal descriptors and complex network modeling. At first, the texture image is modeled as a network. Then, the network is converted into a surface where the Cartesian coordinates and the vertex degree is mapped into a 3D point in the surface. Then, we calculate a description vector of this surface using a method inspired by the Bouligand-Minkowski technique for estimating the fractal dimension of a surface. Specifically, the descriptor corresponds to the evolution of the volume occupied by the dilated surface, when the radius of the spherical structuring element increases. The feature vector is given by the concatenation of the volumes of the dilated surface for different radius values. Our proposal is an enhancement of the classic complex networks descriptors, where only the statistical information was considered. Our method was validated on four texture datasets and the results reveal that our method leads to highly discriminative textural features.

Patterns and randomness in networks for computer vision: from graphs to neural networks

“…This is a classic line of research in the Scientific Computing Group where many texture recognition methods have been developed in the last decade. (16,19,131,154,(199)(200)(201)(202)(203)(204)(205)(206)(207) We discussed this approach in more detail in Chapter 2, Section 2.3.3.1. Here, we describe a new method focusing on one of the latest developments of the approach, (19) where a multilayer network is built for trichromatic (RGB) images.…”

“…32 SEM images were acquired with scales 200 nm and 300 nm, corresponding to sensing units that were subjected to distinct concentrations of PCA3 in addition to the negative sequence (non-complementary) and a blank measurement for control. Afterwards, they are rescaled to 1024 × 768 pixels and cropped using different window sizes (50,100,200,300,400, and 500 pixels), with no overlap. We empirically found that the window size of 300 × 300 pixels was the best approach for training the models (results with other crop dimensions can be consulted in (242)), so we consider this in the following.…”