Bicubic interpolation

About: Bicubic interpolation is a research topic. Over the lifetime, 3348 publications have been published within this topic receiving 73126 citations.

Quadratic interpolation for near-Phong quality shading

Abstract: sketch describes a simple way to set up coefficients to implement quadratic shading in rendering hardware. Quadratic shading interpolates a second-order shading function to provide quality comparable to per-pixel Phong shading, 1 at a fraction of the complexity and with no restrictions on the number of light sources or the type of lighting. Simple adaptive algorithms allow software and hardware to fall back to Gouraud shading. Triangle Preparation Fig. 1 shows a triangle with lighting computed at six positions: vertex colors L, M, and N, and edge midpoint colors Q, R, and S. Any lighting algorithm may be used to produce these colors. Edge midpoint colors need not be computed or transmitted to the rendering hardware if they are similar to the values produced by Gouraud shading. This may be determined by existing adaptive algorithms for subdividing Gouraud shaded triangles. 2 Fig. 1 also defines the M and N vertex coordinates (x1, y1) and (x2, y2), as well as terms i = x2/x1, j = y1/y2, and k = 1–| i j |. The vertex with color L is translated to the origin and must be at a corner of the triangle's bounding box. As in the figure, assign the vertices such that i and j are no greater than 2, which is possible except for co-incident vertices. This reduces the numerical precision required for quadratic shading. Quadratic Function Coefficients We want to define a quadratic shading function I (x, y) = ax 2 + bxy + cy 2 + dx + ey + f that evaluates to the specified color values at the six sample points. Equations (1) define five intermediate color values. Equations (2) define the six coefficients. T/2, U/2, and (T + U-2V)/2 measure the worst-case difference between Gouraud shading and quadratic shading on the three edges, which occurs at edge midpoints. Rendering hardware may compare these to a threshold to select whether to fall back to Gouraud shading. (2) a = 3D 2(T + Uj 2-2Vj) / (k 2 x1 2) b = 3D 4(2V-Ti-Uj-Vk) / (k 2 x1 y2) c = 3D 2(U + Ti 2-2Vi) / (k 2 y2 2) d = 3D (G-Hj) / (k x1) e = 3D (H-Gi) / (k y2) f = 3D L The quadratic shading function may be easily computed using forward differencing. A scanline rendering algorithm requires two additions to compute each intensity. It can be defined …

Subdivision of Box-Splines

Abstract: The two original refinement algorithms for defining subdivision surfaces were based on the biquadratic and bicubic tensor-product B-splines. At about the same time the use of box-splines as a more inclusive extension of B-splines to multivariate interpolation and approximation was being developed, and fairly soon a refinement algorithm over triangulations based on a box-spline was published.

Interpolation Effects on Accuracy of Mutual Information Based Image Registration

Abstract: The image registration inevitably involves interpolation problems to estimate gray values of the image at positions other than the grid points. In this paper interpolation induced effects on the accuracy of registered results are investigated by using a mutual information measure. Three interpolation techniques, namely nearest neighbor interpolation, bilinear interpolation and partial volume interpolation, are investigated under some elaborately designed experiments. The rigid transformation is limited and the simplex search strategy is adopted. The effects of histogram bin numbers and the subsampling rates are also investigated. Experimental results demonstrate that the partial volume interpolation shows much more smoothness of the mutual information function than nearest neighbor and bilinear interpolations. It is much more robust to improve the accuracy than the other two interpolations. The suitable decrease of histogram bin numbers can further smooth the mutual information function and increase the accuracy of the registration results. The decrease of the subsampling rates greatly saves the computation time, and it results in little losses of the accuracy of the final registered results, when using the partial volume interpolation.

Method and apparatus for multi-dimensional interpolation

Abstract: The invention involves selecting a path through a multi-dimensional hyper-cube from a base vertex to an opposite corner or vertex of the hyper-cube. The path is selected by ranking the fractional components of the point or value to be interpolated. An N-dimensional interpolation is performed according to this sequence. During an interpolation a base vertex for an input color value is determined. The output value for the base vertex is accumulated. The fractional values of the input color value are sorted and ranked according to magnitude to produce an interpolation sequence. The interpolations are performed for each axis of the N-dimensions by selecting an axis for interpolation based on the order, performing an interpolation corresponding to the selected axis producing an interpolation result, and accumulating the interpolation result.