W AVELET BASED T EXTURE S YNTHESIS Claire Gallagher and Anil Kokaram Department of Electronic and Electrical Engineering Trinity College Dublin, Ireland. email: gallaghc@mee.tcd.ie Abstract This paper presents a new algorithm for synthesising image texture. Texture synthesis is an im- portant process in image post-production. The best previous approaches have used non-parametric methods for synthesising texture. Unfortunately, these methods generally suffer from high computa- tional cost and difficulty in handling scale in the synthesis process. This paper introduces a new idea of using wavelet decomposition as a basis for non-parametric texture synthesis. The results show an order of magnitude improvement in computational speed and a better approximation of the dominant scale in the synthesised texture. Keywords: Texture Synthesis, Complex Wavelet Transform, Image Processing, Non-parametric Im- age Modeling. Figure 1: Texture synthesis: Given an example texture I e as an input (left), the algorithm aims to reproduce new texture I s (right). 1 Introduction The problem of texture synthesis has been an active research topic in recent years [5, 4, 15, 10]. Given an example of texture as a small subimage, the idea is to create a much larger image by synthesising more texture. Figure 1 shows on the left a typical example image or “seed” of size 128 × 128 and on the right is the synthesised image of size 256 × 256 created by surrounding this “seed” with new texture. This kind of operation is often required in the post-production of digital images when a large area is to be covered with texture that looks like some smaller example. Picture editing often requires filling of missing information and texture synthesis processes like these can fill such holes with reasonable material. The essential idea is to somehow estimate the p.d.f. of the image intensity I (x), denoted by P (I (x )) at a pixel site x =(i, j ). The process of texture synthesis is then a matter of drawing a random sample from that distribution. What makes this difficult is estimating P (I (x )). Two different approaches have