Improved optimization of a modified Hopfield neural network for early vision

This paper proposes a new method to improve the energy optimization of a modified Hopfield neural network that has been used to detect edges of non-uniformly illuminated images. Hopfield showed that artificial neural networks can be used in solving complex optimization problems and minimization problems. Koch et al. have shown how these networks can be generalized to solve the nonquadratic energy functionals of early vision by mapping the binary line processes into continuous variables bounded by 0 and 1. He also outlined one possibility for choosing an associated cost function. Earlier, we have shown that the coefficients in a cost function should not remain fixed for an image with inconsistent illumination and proposed a second-order variation for them. We actually used a changing schedule of these coefficients and reported good detection results by comparing our result with several widely used edge detection methods, both quantitatively and qualitatively. More recently, we observed that the most difficult features to extract from real world 8-bit digital images are those having a gray level difference of 1 to 20 and developed a formula, based upon empirical observation, to assign proper neural net coefficient weights to extract features from this region. This resulted in faster neural network convergences as compared to our earlier method without compromising it's good detection results.