The Atlas Structure of Images

Area of Science:

• Computer Vision
• Image Analysis
• Computational Neuroscience

Background:

• Image analysis often requires isolating and relating image regions of varying detail and extent.
• Existing computer vision methods use downsampling, pyramids, cropping, and patches to handle these challenges.
• A compatible geometric structure with the scale-space model of image measurement is needed.

Purpose of the Study:

• To develop an ideal geometric structure for image region analysis compatible with the scale-space model.
• To establish containment and cause/effect relations between image viewing elements (apertures).
• To demonstrate the utility of this structure for image description and biological vision.

Main Methods:

• Introduction of "apertures" as image viewing elements with fuzzy edges.
• Establishing containment and cause/effect relations to form cross-scale atlases.
• Demonstrating Gaussian apertures as a continuous version of image pyramids and their equivalence to scale-space theory.

Main Results:

• Cross-scale atlases are formed by linking apertures, providing a unified framework for image description.
• Gaussian aperture atlases are a continuous analogue of image pyramids.
• Views through Gaussian apertures approximate derivative of Gaussian filter responses in scale-space theory.

Conclusions:

• The proposed aperture-based geometric structure provides an ideal framework for image analysis.
• This model supports the hypothesis that mammalian V1 simple cells implement local views of the retinal image.
• A novel keypoint descriptor scheme based on this structure outperforms non-learning schemes.