VLSI Systolic Implementation of the Transportation Simplex Algorithm for Texture Distance Computation

Systolic structures, first introduced by Kung and Leiserson in 1978, consist of a large number of simple processing elements, which are connected in a regular way such that higher performance is achieved through extensive concurrent and pipeline use of data items. These structures lend themselves to the involved computations needed in computer vision applications. In the context of texture analysis, a new and effective method for texture representation and classification has been developed by the last author. The method is based primarily on the idea of using a transportation problem-like structure to model the event matching distance, at a given resolution level, is between two histograms each representing the distribution of feature events within an image block of a specific size. The matching process is thus reduced to finding a solution to the streamlined transportation simplex problem. In this paper, a systolic solution to the transportation problem is proposed. A square mesh-connected cells, each having the initial supply and demand values for the row and the column to which it belongs, are used to model the case of n sources and n destinations. Two algorithms, which constitute a solution to the problem, are developed. First, the Russell's technique for selecting an initial basic feasible solution is introduced. Only local communication between a a cell and any of its neighbors is needed. Global commamications between a control unit and the cells are kept to a minimum. The second algorithm tests the optimality of the initial basic feasible solution from the Russell's method. An algorithm for computing the chain reaction caused by increasing the entering basic variable(s) and which iteratively computes the final solution to the problem is then developed. The algorithms are shown to take 0(n/sup 2/) time for execution.