Two frontiers in morphological image analysis: differential evolution models and hybrid morphological/linear neural networks

We briefly describe advancements in two broad areas of morphological image analysis. Part I deals with differential morphology and curve evolution. The partial differential equations (PDEs) that model basic morphological operations are first presented. The resulting dilation PDE, numerically implemented by curve evolution algorithms, improves the accuracy of morphological multiscale analysis by Euclidean disks and (its anisotropic/heterogeneous version) is the basic ingredient of PDE models that solve image analysis problems such as gridless halftoning and watershed segmentation based on the eikonal PDE. Part II deals with morphology-related systems for pattern recognition. It presents a general class of multilayer feedforward neural networks where the combination of inputs in every node is formed by hybrid linear and nonlinear (of the morphological/rank type) operations. For its design a methodology is formulated using ideas from the backpropagation algorithm and robust techniques are developed to circumvent the non-differentiability of rank functions. Experimental results in handwritten character recognition are described and illustrate some of the properties of this new type of neural nets.