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Geometric Back-Propagation in Morphological Neural Networks.

Rick Groenendijk, Leo Dorst, Theo Gevers

IEEE Transactions on Pattern Analysis and Machine Intelligence

|June 29, 2023

Summary

This summary is machine-generated.

This study defines back-propagation for morphological neural networks, showing dilation layers learn geometry. Morphological networks significantly outperform convolutional networks in predictions and convergence.

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Area of Science:

Computer Science
Artificial Intelligence
Machine Learning

Background:

Morphological neural networks offer an alternative to traditional convolutional networks.
Understanding the training dynamics and geometric learning capabilities of these networks is crucial.

Purpose of the Study:

To define back-propagation through geometric correspondences for morphological neural networks.
To investigate the geometric learning properties of dilation layers.
To compare the performance of morphological networks against convolutional networks.

Main Methods:

Definition of back-propagation using geometric correspondences.
Analysis of dilation layers through input/output erosion.
Proof-of-principle implementation and comparison with convolutional networks.

Main Results:

A novel definition for back-propagation in morphological networks is established.
Dilation layers demonstrate the ability to learn probe geometry via erosion.
Morphological networks exhibit superior prediction accuracy and convergence rates compared to convolutional networks.

Conclusions:

The proposed back-propagation method enables effective training of morphological networks.
Morphological networks possess inherent geometric learning capabilities.
These findings suggest morphological networks are a promising alternative for tasks requiring geometric understanding.