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Medical Image Processing with Orientation Scores

Erik Franken

2006 Wolfram Technology Conference
Conference location

Champaign, IL

Measurements conducted on the biological visual system show that the primary visual cortex has cells that respond to structures with a specific orientation, such as lines and edges. Cells that respond to nearly the same orientation appear to be strongly interconnected. This inspires researchers in computer vision to decompose an image in a so-called orientation score, where the orientation parameter is made an explicit dimension. We developed a framework for image segmentation and enhancement in orientation scores, where an important starting point is that an orientation score can be considered as a function on the Euclidean motion group. We developed invertible orientation scores, meaning that the transformation from image to orientation score has a well-posed inverse transformation. Furthermore, we enable operations in the orientation score by considering both linear and nonlinear left-invariant evolution equations on the Euclidean motion group. The evolution equations can be considered as a mathematical model for the Gestalt principles of proximity, good continuation, and closure. Linear evolutions are rendered by performing a convolution operation on the Euclidean motion group. For solving nonlinear evolution equations we consider iterative explicit numerical schemes, where the difficulty lies in obtaining rotational invariance. For the development of all techniques, Mathematica proves to be a powerful tool, enabling us to quickly transfer mathematical equations into implementations. For some algorithms we use MathLink and C++ to gain speed. We will show how we solve specific problems with Mathematica, and provide practical examples on both artificial and medical images. These examples show that the orientation score framework is advantageous for the analysis of strongly oriented patterns, especially at positions where crossings of oriented structures do occur.

*Social Science > Perception
*Wolfram Technology > Linking Technology > MathLink
*Wolfram Technology > Programming > 2D Graphics
*Wolfram Technology > Programming > 3D Graphics
*Wolfram Technology > Special Versions > gridMathematica

image enhancment, BioMM, visual cortex, orientation, image segmentation, Euclidian motion group, Gestalt principles of proximity

ImageProcessingOrientationScores-handouts.pdf (3.7 MB) - PDF Document
ImageProcessingOrientationScores-slides.pdf (6.9 MB) - PDF Document