Learning an artificial neural network to discover bit-quad-based formulas to compute basic object properties

Shape analysis requires estimating object properties in many applications, including optical character recognition, tumor classification, skin cancer recognition, leaf and plant identification, and cell analysis. In particular, bit-quad-based linear expressions proposed by Gray and Duda for calculating the area and perimeter of binary images are widely used in the literature. Nevertheless, these formulas require computing 14 or 15 bit-quad patterns out of 16 possible, becoming critical in applications with limited computing resources. Hence, this paper introduces a method based on a single-layer artificial neural network (ANN) to discover new expressions to calculate the area and perimeter with fewer bit-quads than the original formulas without losing measuring accuracy. Besides, an iterative elimination process removes irrelevant bit-quads whose corresponding weights approach zero. After that, an inductive analysis from observing the learned weights provides interpretable formulas for the area and perimeter. Furthermore, the proposed approach is also applied to find bit-quad-based formulas for directly computing the contact perimeter property, whose original formula requires precomputing Gray's area and perimeter of the object. In addition, aiming to show our method's versatility in other applications, we address a real-world problem to discover a bit-quad-based formula to distinguish between two classes of loss of bone density caused by hyperthyroidism and aging in rats. The experimental results show that the proposed approach reduces by approximately half the bit-quads needed to calculate the area and perimeter of Gray and Duda. Likewise, the number of bit-quads to compute the contact perimeter is reduced from nine to six. Besides, the estimated value on test sets by all the found formulas is the same as their original counterparts. On the other hand, the classification of loss of bone density type using the found bit-quad-based formula reaches an accuracy of 100% in the test set. Therefore, the proposed method is an alternative to finding linear expressions with few bit-quads to measure basic object properties.