Extending the Morphological Hit-or-Miss Transform to Deep Neural Networks

Area of Science:

• Computer Vision
• Deep Learning
• Mathematical Morphology

Background:

• Deep learning predominantly uses convolutional architectures.
• Morphology offers an alternative foundation for geometric analysis and interpretability.
• The hit-or-miss transform is a morphological operation considering foreground and background information.

Purpose of the Study:

• To address limitations in existing neural hit-or-miss definitions.
• To formulate an optimization problem for learning the hit-or-miss transform in deep architectures.
• To introduce a novel morphologically inspired generalized convolution.

Main Methods:

• Formulated an optimization problem for the hit-or-miss transform.
• Modeled the non-empty intersection of structuring elements and introduced Don't Care regions.
• Analyzed convolution as a semantic hit-to-miss transform.
• Developed a generalized convolution based on morphological principles.

Main Results:

• The direct encoding hit-or-miss transform offers improved interpretability of learned shapes.
• The proposed generalized convolution outperforms conventional convolution on benchmark datasets.
• Quantitative experiments validate performance on synthetic and real-world data.

Conclusions:

• Morphology provides a valuable alternative to convolution in deep learning.
• The developed hit-or-miss transform enhances shape understanding and classification.
• This work bridges mathematical morphology and deep learning for advanced image analysis.