Four new trigonometric Bernstein-like bases with two denominator shape parameters (DTB-like basis) are constructed, based on which a kind of trigonometric Bézier-like curve with two denominator shape parameters (DTB-like curves) that are analogous to the cubic Bézier curves is proposed. The corner cutting algorithm for computing the DTB-like curves is given. Any arc of an ellipse or a parabola can be exactly represented by using the DTB-like curves. A new class of trigonometric B-spline-like basis function with two local denominator shape parameters (DT B-spline-like basis) is constructed according to the proposed DTB-like basis. The totally positive property of the DT B-spline-like basis is supported. For different shape parameter values, the associated trigonometric B-spline-like curves with two denominator shape parameters (DT B-spline-like curves) can be C2 continuous for a non-uniform knot vector. For a special value, the generated curves can be C(2n-1)  (n=1,2,3,…) continuous for a uniform knot vector. A kind of trigonometric B-spline-like surfaces with four denominator shape parameters (DT B-spline-like surface) is shown by using the tensor product method, and the associated DT B-spline-like surfaces can be C2 continuous for a nonuniform knot vector. When given a special value, the related surfaces can be C(2n-1)  (n=1,2,3,…) continuous for a uniform knot vector. A new class of trigonometric Bernstein–Bézier-like basis function with three denominator shape parameters (DT BB-like basis) over a triangular domain is also constructed. A de Casteljau-type algorithm is developed for computing the associated trigonometric Bernstein–Bézier-like patch with three denominator shape parameters (DT BB-like patch). The condition for G1 continuous jointing two DT BB-like patches over the triangular domain is deduced.

Abstract. In order to solve the problem of the detail and the indistinct texture of the traditional image fusion algorithm, an image fusion method based on non-subsampled contourlet transform (NSCT) and self-adaptive correlation coefficient operator is proposed, which can effectively preserve the details of the fusion source image information and important structural information. Firstly, the low-pass subband and band-pass subband of the source image are decomposed by NSCT, and then the low-pass subband is fused by the fusion rule of the adaptive region variance, the band-pass subbands are fused by adaptive weights with coefficients gradient as the factor. Finally, through the NSCT inverse transformation to get the result image. The simulation results show that the adaptive algorithm is superior to the fusion method of human control fusion rule.

When the traditional Hough transform based on circle detection locates the human iris, it involves a three-dimensional parameter space, so there is a shortage of computational time and space overhead. Aiming at this problem, a Hough transform circle detection algorithm using gradient to reduce the spatial dimension of parameters is proposed. Firstly, the image is preprocessed by mathematical morphology to reduce noise and eyelash interference. Secondly, the ant colony optimization algorithm is used to preprocess the image. Edge extraction is performed to reduce the number of points participating in the Hough transform. Finally, the improved Hough transform is used to locate the iris. The high-quality and low-quality images are used to compare the traditional Hough transform method and the literature [13] method. The results show that the method not only improves the positioning speed, but also improves the positioning accuracy. Compared with other methods, the image quality is improved. The requirements are also significantly reduced.

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