Optical EngineeringBoundary value problem of image modification
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The concept of the boundary value problem into image processing is introduced and an image modification technique is presented that works under the condition that the transformation function for a set of pixels is given a priori. For example, if adjoining pictures are taken separately under different illumination and then put together into a single picture, processing the whole picture uniformly can result in some artifacts along the seams, across which image features change abruptly. To resolve this problem, the image features of the border pixels should be transformed to be continuous with the neighboring pictures. Thus, the transformation function for such pixels should be set a priori to meet the above condition, and for the remaining pixels it should be adjusted accordingly. The same technique can be applied to a single picture. For example, if a picture is taken under nonuniform illumination, which causes some regions of the picture to be dark and others to be light, the ransformation function for those regions should be given as boundary conditions. Then the function at any pixel is interpolated from the boundary values. An interactive technique is discussed for giving the boundary conditions and for determining the image transformation function.