The Hermite transform as an efficient model for local image analysis: An application to medical image fusion

The Hermite transform is introduced as an image representation model that can be used to tackle the problem of fusion in multimodal medical imagery. This model includes some important properties of human visual perception, such as local orientation analysis and the Guassian derivative model of early vision. Local analysis is achieved by windowing the image with a Gaussian function, then a local expansion into orthogonal polynomials takes place at every window position. Expansion coefficients are called Hermite coefficients and it is shown that they can be directly obtained by convolving the image with Gaussian derivative filters, in agreement with psychophysical insights of human visual perception. A compact representation can be obtained by locally steering the Hermite coefficients towards the direction of local maximum energy. Image fusion is achieved by combining the steered Hermite coefficients of both source images with the method of verification of consistency. Fusion results are compared with a competitive wavelet-based technique, proving that the Hermite transform provides better reconstruction of relevant image structures.