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Standard morphing algorithms utilize a source image, a destination image and two 2D arrays of coordinates. The first array, S, specifies the coordinates of control points in the source image. The second array, D, specifies the corresponding positions in the destination image. Both S and D must have the same dimensions in order to establish a one-to-one correspondence. Morphed images are processed through a 2-pass warping with 2 output intermediate images I1 and I2. The first pass is responsible for resampling each row independently. It maps all initial point coordinates (u, v) to their (x, v) coordinates in the intermediate image, thereby positioning each input in the proper output column. The second pass then resamples each column in the intermediate image, mapping every (x, v) point to its final (x, y) position in I1/I2. The 2D array is where the control points are stored to impose a topology to the mesh. More detail is add to each frame by a transformation using an interpolated mesh M as the set of target positions for the input mesh points. M is computed by performing a linear transformation between the respective points in S and D. The "warp" program actually plays an important role since both I1 and I2 are each warped using M as the target mesh. Thus, I1 is warped using meshes S ad M. In addition, I2 is warped using meshes D and M. Once the landmarks of the source and target images are aligned, they are cross-dissolved to generate a morph frame. After applying this standard morphing approach to a set of VHM images with disappointing results, we began to explore alternative algorithms to accomplish the morphing process.
We already possessed a highly detailed set of segmentation data that included most of the gross anatomical structures identifiable within the image resolution of the VHM images data set. We set out to determine how this segmentation data could be used to control the morphing process. A point-to-point method was developed that considered every pixel in the each of the control and destination images. With this new approach, we first visited each point (x, y) of the segmentation data set to obtain the structure classification numbers for each pixel of both the control and destination image (id1 and id2). New segmentation data for intervening images was then calculated by following one of the following cases:
Case 1: If id1=id2, there was no doubt that all corresponding points in the all of the intervening images would be assigned as the same structure. Our assumption here is that pixels of each segmented structure would have similar RGB color values. Therefore we could register this point (x, y) for the classification number and use the RGB color value of the control and destination images to calculate the corresponding point value of each of the intervening images.
Case 2: If id1 did not equal id2 the program would locate the nearest neighbor (x1, y1) for id1 in the control image and the nearest neighbor (x2, y2) for the destination image. We then assume that all pixels located at (x, y) in the any intervening morphed images would be limited to either id1 or id2. To determine which points were to be assigned id1 and which to id2, we determine the two nearest neighbors, line them up and calculate the intersection. A horizontal line was drawn through the intersection for use in assigning structure identification numbers to each of the pixel of intervening images. Points above the line were assigned id1 and those below id2. Completion of this process results in a newly established set of segmentation data for each morphed image being generated. During the morphing process this new segmentation data was applied in the morphing of each of the calculated image. RGB color values for morphed images pixels that fell above the horizontal line were calculated from pixel (x, y) of the control image and pixel (x1, y1) of the destination image. Values below the line were calculated from pixels (x2, y2) of the control image and (x, y) of the destination image.
By applying this new technique we are able to produce high-resolution morphed images that we believe maintains a high level of anatomical accuracy. These images are of sufficient quality for use in filling the anatomical gaps that resulted in both the Visible Human Male and Female during the sectioning process. As noted, an added benefit of this new approach is that we not only obtained the morphed raster images, but also simultaneously derived an accurate and complete set of segmentation for each of the newly formed image. Anatomical accuracy obviously is a factor of concern with the production of morphed images. For this reason we inserted each of the morphed images along with its corresponding segmentation data into our 3D visualization programs and generated both volumetric and surface models for visual confirmation of anatomical accuracy.
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