An Introduction to Deep Morphological Networks

Keiller Nogueira,Mauro Dalla Mura,Jocelyn Chanussot,Jefersson A Dos Santos

doi:10.1109/access.2021.3104405

Abstract

Over the past decade, Convolutional Networks (ConvNets) have renewed the perspectives of the research and industrial communities. Although this deep learning technique may be composed of multiple layers, its core operation is the convolution, an important linear filtering process. Easy and fast to implement, convolutions actually play a major role, not only in ConvNets, but in digital image processing and analysis as a whole, being effective for several tasks. However, aside from convolutions, researchers also proposed and developed non-linear filters, such as operators provided by mathematical morphology. Even though these are not so computationally efficient as the linear filters, in general, they are able to capture different patterns and tackle distinct problems when compared to the convolutions. In this paper, we propose a new paradigm for deep networks where convolutions are replaced by non-linear morphological filters. Aside from performing the operation, the proposed Deep Morphological Network (DeepMorphNet) is also able to learn the morphological filters (and consequently the features) based on the input data. While this process raises challenging issues regarding training and actual implementation, the proposed DeepMorphNet proves to be able to extract features and solve problems that traditional architectures with standard convolution filters cannot.

Highlights

Over the past decade, Convolutional Networks (ConvNet) [1] have been a game changer in the computer vision community, achieving state-of-the-art in several computer-vision applications, including image classification [2], [3], object and scene recognition [4]–[8], and many others
Please remember that we present a proof of concept of a new paradigm: using non-linear morphological operations instead of standard linear convolutions for a deep network
It is possible to observe that the DeepMorphNet produced a more consistent prediction map than the ConvNet baseline

Summary

Introduction

Convolutional Networks (ConvNet) [1] have been a game changer in the computer vision community, achieving state-of-the-art in several computer-vision applications, including image classification [2], [3], object and scene recognition [4]–[8], and many others. This deep learning technique may be composed of several distinct components (such as convolutional and pooling layers, nonlinear activation functions, etc), its core operation is the convolution, a linear filtering process whose weights, in this case, are to be learned based on the input data. In literature [19], [20], this definition is performed experimentally (with common shapes being squares, disks, diamonds, crosses, and x-shapes), an expensive process that does not guarantee a good descriptive representation

Methods

Results

Conclusion