Geometry and Radiometry Invariant Matched Manifold Detection

Area of Science:

• Computer Vision
• Machine Learning
• Image Processing

Background:

• Deformable objects present challenges in computer vision due to complex geometric and radiometric transformations.
• Existing methods like universal manifold embedding (UME) map object appearances to distinct linear subspaces, assuming finite-dimensional geometric deformations.
• Generalizing UME to include affine geometric and monotonic radiometric transformations is crucial for broader applications.

Purpose of the Study:

• To generalize the universal manifold embedding (UME) framework to handle both affine geometric and monotonic radiometric transformations.
• To present a novel framework for the detection and recognition of deformable objects under these complex transformations.
• To develop a method where object representation is invariant to both geometric and radiometric changes.

Main Methods:

• Developed a novel framework that applies an operator to observations, rendering them invariant to monotonic amplitude transformations while maintaining covariance with affine transformations.
• Utilized the universal manifold embedding (UME) to map all possible observations of an object into a single linear subspace, invariant to both geometric and radiometric transformations.
• Tessellated observed surfaces into tiles, approximating local deformations with affine geometric and monotonic intensity transformations, and solved detection/tracking by evaluating distances between subspaces.

Main Results:

• The generalized UME framework successfully maps deformable objects undergoing affine geometric and monotonic radiometric transformations into distinct, invariant linear subspaces.
• The proposed method achieves invariance to both geometric and radiometric transformations, creating a universal object representation.
• Detection and tracking are effectively solved by computing distances between these linear subspaces, demonstrating robustness.

Conclusions:

• The developed framework provides a universal and invariant representation for deformable objects, significantly advancing detection and recognition capabilities.
• The method's ability to handle complex geometric and radiometric deformations by mapping them to linear subspaces offers a powerful approach for computer vision tasks.
• Classification is efficiently performed by determining the closest labeled subspace in a Grassmannian, showcasing the practical utility of the UME generalization.