# Agents, complex networks and partial differential equations: integrating models to texture analysis

## Members

### Bruno Brandoli Machado, Odemir M. Bruno

## Introduction

Methods to describe textures have an important role in image analysis and computer vision. Most of the traditional methods in the literature are based on either statistical approaches or established models, and usually, fail in describing different textures in the images. In this project, we intend to develop an approach able to represent patterns by means of agents combined with complex networks. This approach is completely original when we integrate to the agents and to the nets the multi-scale representation (decomposition) using non linear partial differential equations (PDEs).

In this study, we propose a novel approach for texture modeling based on partial differential equation (PDE). An initial image I is decomposed into a family of derived sub-images. We then compute two components: the u component obtained with anisotropic diffusion and the v component which is calculated by the difference between the original image and the u component.

A texture with several levels of decomposition is shown in Figure 1. The first row shows the family of cartoon approximations from the original image I. We can observe that the information is gradually smoothed, while textures, in third row, are enhanced by the difference between the original image and cartoon approximations. The solution of the heat diffusion is depicted in rows 2 and 4. Note that the distribution of heat corresponds to grey values in the image and the diffusion time is represented by the number of iterations t. For different scales t we obtain different levels of smoothing, as shown from t1 (Figure 1(b)) to t5 (Figure 1(f)).

PDE: Description coming soon. | |

Agents for texture analysis Description coming soon. | |

COMPLEX NETWORKS: Description coming soon. |