This paper proposes an idea of combining the Meyer Shearlet and mathematical morphology to produce the edge detection of pathological sections of the colon. First, the method of constructing a class of sufficiently smooth sigmoid functions along with its relative scale function and Meyer wavelet function is provided in this paper. Based on those, in order to get the new Meyer wavelet function, we use the sigmoid function to construct more general scale functions. Next, taking sufficiently

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... sigmoid functions as examples, combining the relative Meyer wavelet and Shearlet to denoise some pathological sections of the colon leads a decent feedback. At last, this paper provides an improved algorithm for the edge detection of mathematical morphology with the background of multiscale and multistructure. This algorithm is used to carry out the edge detection of images after denoising yields a new edge detection algorithm that fuses the Meyer Shearlet denoising and mathematical morphology. According to the simulation results, the new algorithm is more beneficial for the observation and diagnosis of doctors since the edge noise of the colon pathological image detected by the new algorithm is smaller and provides more continuous and clear lines. Therefore, the fusion algorithm provided in this paper is an effective way to carry out the edge detection of an image.