Multifocus Image Fusion using the Haar wavelet transform C. Toxqui-Quitl, A. Padilla-Vivanco * and G. Urcid-Serrano Instituto Nacional de Astrofísica, Óptica y Electrónica, Luis Enrique Erro #1, Tonanzintla, Apartado Postal, 51 y 216. C. P. 72000. Puebla. México. ABSTRACT We present the multifocus image fusion based in the Haar transformation of an image. The rows of the matrix transformation are computed by means the dyadic scaling and translating of the Haar function. The Haar transformation matrix is fast, real and orthogonal. These properties are advantages for image processing, particularly in image fusion. A multifocus fusion example using the Haar transform is presented. Keywords: Wavelets, Haar transform, image fusion. 1. INTRODUCTION Image fusion is the digital technique for merging two or more images from different sensors to obtain complementary information as sharp or interest regions of each image for purposes of the visual system and computer processing [1-3]. The fusion objective is to obtain a new image with the several features of the source images. Fusion image is often required for images from different acquisition modalities of the same scene or objects. The easier fusion method is the average between the corresponding pixels of the images under study. However, the contrast in the final fused image is commonly low when this method is applied. So that, the features contrast in each image is reduced. A solution is to use the Wavelet transform coefficients under a specific fusion rule and from it; the inverse wavelet transform is computed. It results in a better preservation of borders and complementary information of the scenes and the objects of interest. 2. DYADIC WAVELETS: A REVIEW In this section we introduce the mathematical concepts for implementing the discrete wavelet transform. This transform has a kernel based in a wavelet function. The basis set of wavelet functions (29 { } x b a, ψ in which we are interested is like- measured, with compact support and square integrable over the real line, ) ( 2 ℜ L so that ) ( ) ( 2 ℜ ∈ 2200 L x n ψ , the function satisfy that ∫ ∞ ∞ - ∞ < dx x b a 2 , ) ( ψ . (1) where a >0 and ℜ ∈ b . In Wavelet analysis, it is possible to generate a basis functions set, dilating and translating a prototype function, ψ(x), called the basic wavelet. So that, the functions set (29 { } x b a, ψ can be generated by translations b and scaling a from the basic wavelet ψ(x) as follows (29       - = a b x a x b a ψ ψ 1 , . (2) * apadilla@inaoep.mx ; phone: 52 222 2 66 31 00; fax 52 222 2 47 29 40; inaoep.mx SPIE USE, V. 5 5558-112 (p.1 of 8) / Color: No / Format: A4/ AF: A4 / Date: 2004-07-14 17:18:45 Please verify that (1) all pages are present, (2) all figures are acceptable, (3) all fonts and special characters are correct, and (4) all text and figures fit within the margin lines shown on this review document. Return to your MySPIE ToDo list and approve or disapprove this submission.