Advanced Computer Vision & Image Processing using PDEs and Active Contours

(3-0-0-3)

CMPE Degree: This course is Not Applicable for the CMPE degree.

EE Degree: This course is Not Applicable for the EE degree.

Lab Hours: 0 supervised lab hours and 0 unsupervised lab hours.

Technical Interest Group(s) / Course Type(s): Systems and Controls

Course Coordinator:

Prerequisites: ECE 6550

Catalog Description

Algorithms for computer vision and image processing, emphasizing partial-differential equation and active contour methods. Topics include image smoothing and enhancement, edge detection, morphology, and image reconstruction.

Textbook(s)

Course Outcomes

Not Applicable

Strategic Performance Indicators (SPIs)

Outcome 1 (Students will demonstrate expertise in a subfield of study chosen from the fields of electrical engineering or computer engineering):
1. Mathematically formulate customized PDE based solutions to image processing and computer vision problems by leveraging variational methods as well as differential geometry in cases where shape is relevant.

Outcome 2 (Students will demonstrate the ability to identify and formulate advanced problems and apply knowledge of mathematics and science to solve those problems):
1. Discretize mathematical PDE solutions into finite difference equations that can be implemented on the computer, ensuring both numerical stability and convergence.

Outcome 3 (Students will demonstrate the ability to utilize current knowledge, technology, or techniques within their chosen subfield):
1. Effectively implement discretized PDE solutions in their language of choice (MATLAB, C++, fortran, Java, Python, etc.).

Topical Outline

Brief PDE Background
* Introductory theory for linear partial differential equations
* Algorithms and issues for numerical implementation

Nonlinear Image Denoising and Enhancement Algorithms
* Greyscale Image Smoothing using Anisotropic Diffusion
* Continuous Morphology Methods for Grayscale Images

Design of Nonlinear Image Filters using the Calculus of Variations

Active Contour Methods
* Differential geometry for curves
* Snakes (parametric active contours)
* Geometric active contours (curve evolution)
* Level Set Methods (implicit active contours)

Advanced Computer Vision Algorithms
* Image segmentation using active contours
* Optical flow and steory disparity estimation using PDE's.
* Variational Approaches to Image Registration
* Visual Tracking with Active Contours

3D Surface Reconstruction Algorithms
* Differential geometry for surfaces
* Volumetric Image Segmentation using Active Surfaces
* Variational Approaches to Shape from Shading
* Multi-view Stereo Surface Reconstruction

Color Image Processing
* Multi-channel versus geometric modeling of color imagery
* Color Image Denoising, Inpainting, Smoothing, and Enhancement

Shape Analysis
* Shape Comparison and Matching
* Shape Morphing
* Shape correspondence algorithms