graymorphlow.c Low-level grayscale morphological operations void dilateGrayLow() void erodeGrayLow() We use the van Herk/Gil-Werman (vHGW) algorithm, [van Herk, Patt. Recog. Let. 13, pp. 517-521, 1992; Gil and Werman, IEEE Trans PAMI 15(5), pp. 504-507, 1993.] This was the first grayscale morphology algorithm to compute dilation and erosion with complexity independent of the size of the structuring element. It is simple and elegant, and surprising that it was discovered as recently as 1992. It works for SEs composed of horizontal and/or vertical lines. The general case requires finding the Min or Max over an arbitrary set of pixels, and this requires a number of pixel comparisons equal to the SE "size" at each pixel in the image. The vHGW algorithm requires not more than 3 comparisons at each point. The algorithm has been recently refined by Gil and Kimmel ("Efficient Dilation Erosion, Opening and Closing Algorithms", in "Mathematical Morphology and its Applications to Image and Signal Processing", the proceedings of the International Symposium on Mathematical Morphology, Palo Alto, CA, June 2000, Kluwer Academic Publishers, pp. 301-310). They bring this number down below 1.5 comparisons per output pixel but at a cost of significantly increased complexity, so I don't bother with that here. In brief, the method is as follows. We evaluate the dilation in groups of "size" pixels, equal to the size of the SE. For horizontal, we start at x = "size"/2 and go (w - 2 * ("size"/2))/"size" steps. This means that we don't evaluate the first 0.5 * "size" pixels and, worst case, the last 1.5 * "size" pixels. Thus we embed the image in a larger image with these augmented dimensions, where the new border pixels are appropriately initialized (0 for dilation; 255 for erosion), and remove the boundary at the end. (For vertical, use h instead of w.) Then for each group of "size" pixels, we form an array of length 2 * "size" + 1, consisting of backward and forward partial maxima (for dilation) or minima (for erosion). This represents a jumping window computed from the source image, over which the SE will slide. The center of the array gets the source pixel at the center of the SE. Call this the center pixel of the window. Array values to left of center get the maxima(minima) of the pixels from the center one and going to the left an equal distance. Array values to the right of center get the maxima(minima) to the pixels from the center one and going to the right an equal distance. These are computed sequentially starting from the center one. The SE (of length "size") can slide over this window (of length 2 * "size + 1) at "size" different places. At each place, the maxima(minima) of the values in the window that correspond to the end points of the SE give the extremal values over that interval, and these are stored at the dest pixel corresponding to the SE center. A picture is worth at least this many words, so if this isn't clear, see the leptonica documentation on grayscale morphology.
void dilateGrayLow ( l_uint32 *datad, l_int32 w, l_int32 h, l_int32 wpld, l_uint32 *datas, l_int32 wpls, l_int32 size, l_int32 direction, l_uint8 *buffer, l_uint8 *maxarray )
dilateGrayLow() Input: datad, w, h, wpld (8 bpp image) datas, wpls (8 bpp image, of same dimensions) size (full length of SEL; restricted to odd numbers) direction (L_HORIZ or L_VERT) buffer (holds full line or column of src image pixels) maxarray (array of dimension 2*size+1) Return: void Notes: (1) To eliminate border effects on the actual image, these images are prepared with an additional border of dimensions: leftpix = 0.5 * size rightpix = 1.5 * size toppix = 0.5 * size bottompix = 1.5 * size and we initialize the src border pixels to 0. This allows full processing over the actual image; at the end the border is removed. (2) Uses algorithm of van Herk, Gil and Werman
void erodeGrayLow ( l_uint32 *datad, l_int32 w, l_int32 h, l_int32 wpld, l_uint32 *datas, l_int32 wpls, l_int32 size, l_int32 direction, l_uint8 *buffer, l_uint8 *minarray )
erodeGrayLow() Input: datad, w, h, wpld (8 bpp image) datas, wpls (8 bpp image, of same dimensions) size (full length of SEL; restricted to odd numbers) direction (L_HORIZ or L_VERT) buffer (holds full line or column of src image pixels) minarray (array of dimension 2*size+1) Return: void Notes: (1) See notes in dilateGrayLow()
Zakariyya Mughal <email@example.com>
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