Wavelets and their Applications

Chapter 8

Image Processing with Wavelets

8.1. Introduction

The applications of wavelets in image processing are often synonymous with compression. Today, the need for storing large quantities of information and for fast transmission through international communication networks are key issues. This is why two examples of wavelet used in this field have had a particularly pronounced impact:

– for fingerprint storage, the FBI finally chose an algorithm containing wavelets [BRI 95];

– more recently, the compression standard JPEG 2000 [JPE 00] has also been built around algorithms containing wavelets.

These successes had a resounding echo and contributed to the popularization of wavelets. For this reason, the last part of this chapter is devoted to what remains the main 2D-wavelet application: compression.

Before focusing on this point this chapter gives a rapid presentation of the theoretical framework and considers two of the more marginal but still efficient 2D-wavelet applications. We introduce the concepts of decomposition, approximation and detail for an image. They then play a crucial role in:

– the edge detection. In this part we illustrate the capacity of wavelets to locally analyze the fluctuations of image grayscale levels. The processed examples show that, almost without processing, the analysis of images by wavelets makes it possible to extract a new image, from which we can isolate the edges;

– the fusion of images¹. Here we crucially use the local character of wavelet ...