Two-dimensional refinement scheme of direction-based interpolation with discrete orthogonal polynomial decomposition
In this paper, a novel direction-based interpolation approach with discrete orthogonal polynomial decomposition is introduced. A 2D digital image is usually regarded as a sampling of an underlying 2D continuous function, which is called an image field. When the image field is considered as a scalar potential field, the interpolation problem is converted to that if the values at some points in a potential field are given, how to estimate the value of any point more accurately. Both the edges of the image and the content of the objects are well preserved if the image is interpolated along the equipotential lines instead of the coordinate axes. In this study, the equipotential direction at each pixel in the interpolated plane is calculated from the partial derivatives of the discrete orthogonal polynomial decomposition of the original image. For each point, the equipotential line through it is searched in a step-by-step way, guided by the equipotential directions. The value of a point is interpolated linearly from the values of points with known values along the equipotential line. Refinement scheme is applied to interpolate the images to the desired scale. Experiments on a set of CT images show that this method not only preserves the shape structure efficiently even for the objects with complicated structures but also has a low time complexity.
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