Designing Perceptrons for the Recognitionof

Digital straight lines can be charactarized by Rosenfeld's chord property as well as Hung's evenness property. Both properties can be formulated in terms of linear inequalities. Because linear inequalities can be veriied by the predicates of a Gamba perceptron, this leads in a straightforward manner to the design of perceptrons that can recognize digital straight lines. In this paper we will discuss one important aspect of the design process: How can we make the number of perceptron predicates as small as possible? We propose one particular technique to solve this problem. It is based on logical implications between inequalities. For each chord property based perceptron we construct a pruning graph with the logical implications between inequalities as pruning rules. Pruning back predicates according to these rules then leads to a perceptron of size smaller than the original. It seems diicult to give an analytical expression for the exact number of predicates after reduction, because it depends on some intricate number theoretical properties of the length of the line segment. Experimental results for line segment lengths up to L = 240 seem to show that the number of predicates after reduction is close to L 2 =4, whereas the unreduced perceptron contains O(L 3) predicates.