For line, square, or rectangle structuring elements more than 8 pixels wide, the block implements a Van Herk algorithm. All pixels in the structuring element must be set to one. The block decomposes the structuring element into rows and serially finds the minimum pixel value of each row by using the Van Herk algorithm. If the size of the input frame is not a multiple of m pixels, the line memory also adds horizontal padding to a multiple of m. This implementation uses only three comparators total for all rows. Then, if there is more than one row, it calculates the minimum pixel value of the row results by using a comparison tree. The diagram indicates the latency of each computation block.

The Van Herk kernel computes a running forward minimum and a running backward minimum of the pixel values in each row of the neighborhood. For this computation, the pixels in the row must be buffered and the order reversed. The buffer adds latency relative to the comparison tree implementation. The Mirror Buffer is a ping-pong RAM of m pixels, where one memory reads values in reverse order while the other memory is writing. The kernel uses 3+n-1 comparators.

For structuring elements smaller than 8 pixels wide or with one or more pixels set to zero, the block implements a comparison tree.

The diagram shows the architecture of the erosion operation. The algorithm finds the minimum pixel value of each row of the neighborhood in parallel. Then it calculates the minimum pixel value of the rows using another comparison tree. The diagram indicates the latency of each computation block.

For a rectangular neighborhood that is m pixels wide, the first-stage comparison trees contain m – 1 comparators over log₂(m) clock cycles. For instance, for a rectangular neighborhood that is 7 pixels wide, the comparison tree has six comparators over 3 clock cycles.

If the neighborhood you specify contains zeroes, the generated HDL excludes the comparator for the zero locations. The pipeline delay through the comparison tree does not change. For instance, for a nonrectangular neighborhood with a row of [0 0 1 1 0 0 1], the comparison tree for that row contains two comparators and still uses 3 clock cycles.

The latency of the operation is the line buffer latency plus the latency of the kernel calculation. The line buffer latency includes edge padding.

The latency of a Van Herk kernel for a neighborhood of m-by-n pixels is 2m + log₂(n). The block implements this kernel for line, square, or rectangle structuring elements more than 8 pixels wide, with no pixels set to zero.

The latency of a comparison tree kernel for a neighborhood of m-by-n pixels is log₂(m)+log₂(n). The block implements this kernel for structuring elements smaller than 8 pixels wide or with one or more pixels set to zero.