MToS: A Tree of Shapes for Multivariate Images

Area of Science:

• Computer Vision and Image Processing
• Multivariate Data Analysis
• Pattern Recognition

Background:

• Topographic maps (trees of shapes) offer hierarchical image representation, invariant to contrast changes, but are limited to grayscale images.
• Existing methods for multivariate images, like marginal processing, lack satisfactory contrast invariance and self-duality.
• The need for a robust representation for complex image data, including color and hyperspectral images, is critical.

Purpose of the Study:

• To develop a novel tree-based representation for multivariate images.
• To achieve contrast invariance and self-duality for multivariate image analysis.
• To demonstrate the utility of this representation in various image processing tasks.

Main Methods:

• A new method for building a tree-based representation for multivariate images is proposed.
• The method relies on the inclusion relationship between shapes, avoiding arbitrary pixel value ordering.
• The representation is designed to be contrast-invariant and self-dual.

Main Results:

• The proposed tree-based representation successfully extends the properties of gray-level trees of shapes to multivariate images.
• The method demonstrates effectiveness across diverse applications including filtering, segmentation, and object recognition.
• Successful application on various data types: color images, document images, hyperspectral satellite data, multimodal medical images, and videos.

Conclusions:

• The developed method provides a powerful, contrast-invariant, and self-dual representation for multivariate images.
• This approach overcomes the limitations of traditional methods for complex image data.
• The representation opens new possibilities for advanced image analysis and pattern recognition in diverse scientific fields.