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## 1.2 Data Structures

The Hoshen-Kopelman (HK) algorithm (Hoshen and Kopelman, 1976) is a one-pass approach to cluster identification that utilizes two working arrays, matrix and csize, to store the post-processed input map and interim cluster statistics. Post-processed refers to the map resulting from pre-processing - which filters data values not corresponding to the chosen map class. The original input ERDAS/Lan map is read into a holding buffer, filtered, and moved into the matrix array for final processing. This three-step process is referred to as pre-processing. The algorithm traverses the map from left to right, and then from top to bottom, assigning a temporary cluster label (integer) to each non-zero pixel and recording any pixel label or cluster membership changes in the two working arrays. Temporary label assignment is a function of the enforced neighborhood rule and the algorithm implementation, which are explained in detail in Sections 1.3 and 1.4, respectively. Matrix is a two dimensional integer array of size , where n is the height (rows) and m is the width (columns) of the map in pixels. The dimensions n and m are increased by 1 to accommodate boundary columns and rows, containing unique boundary integer values, that are necessary for this implementation. Six integer pointers ( firstRow, secondRow, lastRow, current, west, and north) are maintained to traverse the array and make changes when necessary. Pointers are used to index the matrix array and to minimize the overhead of base-plus-offset array indexing.

Figure 4: The csize working array illustrating either a positive or negative value for each index in the array. Positive values are a count of the pixels in the cluster labeled with the array index value and negative values are pointers to other indexes in the array. Negative indexes can follow a non-circular, recursive path for a finite number of steps.

Integer storage (32 bits/pixel) is required because the matrix array serves a dual purpose. First, matrix holds the post-processed map data, and second, it serves as a working array for the pixels' temporary cluster label. If it is impossible to store the entire matrix array in memory, a divide-and-conquer approach can be implemented whereby cluster identification is performed by partitioning the map along row boundaries and merging the results of each partition. Each partition is of size where k is the number of rows in each partition. If n is not evenly divisible by k, the last partition would have less than k rows.

An integer array (csize) is used to store either the running total of cluster size or an index value for another entry in the csize array. If the stored value is positive, it is the running total of the pixel membership in that cluster. If it is negative, the absolute value of the stored number is an index to the true cluster label. Negative indexes can follow a non-circular, recursive path for a finite number of steps. Figure 4 illustrates the csize working array displaying the positive or negative entries for each index in the array. Temporary cluster 1 shows a membership of 12 pixels whereas temporary cluster 2 is the beginning of a 5-step pointer path () pointing to temporary cluster 3 containing 22 pixels. The existence of the path signifies that the temporary cluster at the head of the path (array index 2) had been previously merged into the temporary cluster at the tail of the path (array index 3). For example, as the result of four independent merge operations, temporary cluster 2 had previously been merged into temporary cluster 3. Compression of this path is significant to the overall efficiency of the FSM implementation and is discussed in more detail in Section 1.5.2.

Next: Neighborhood Rule Up: Hoshen-Kopelman Algorithm Previous: Pre-Processing the ERDAS/Lan

Michael W. Berry (berry@cs.utk.edu)
Sat Mar 30 23:40:13 EST 1996