Advanced Computer Vision & Image Processing using PDEs and Active Contours


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

Corequisites: None.

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.


Course Outcomes

Not Applicable

Student Outcomes

In the parentheses for each Student Outcome:
"P" for primary indicates the outcome is a major focus of the entire course.
“M” for moderate indicates the outcome is the focus of at least one component of the course, but not majority of course material.
“LN” for “little to none” indicates that the course does not contribute significantly to this outcome.

1. ( Not Applicable ) An ability to identify, formulate, and solve complex engineering problems by applying principles of engineering, science, and mathematics

2. ( Not Applicable ) An ability to apply engineering design to produce solutions that meet specified needs with consideration of public health, safety, and welfare, as well as global, cultural, social, environmental, and economic factors

3. ( Not Applicable ) An ability to communicate effectively with a range of audiences

4. ( Not Applicable ) An ability to recognize ethical and professional responsibilities in engineering situations and make informed judgments, which must consider the impact of engineering solutions in global, economic, environmental, and societal contexts

5. ( Not Applicable ) An ability to function effectively on a team whose members together provide leadership, create a collaborative and inclusive environment, establish goals, plan tasks, and meet objectives

6. ( Not Applicable ) An ability to develop and conduct appropriate experimentation, analyze and interpret data, and use engineering judgment to draw conclusions

7. ( Not Applicable ) An ability to acquire and apply new knowledge as needed, using appropriate learning strategies.

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.).

Course Objectives

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