Course syllabus for Image processing

Mathematical analysis in several variables and statistics, and experience with Matlab.

The aim of this course is for students to become familiar with a wide variety of techniques in modern Image Processing. These techniques can be used to subjectively improve image quality for the end-user (image enhancement), remove known image distortions (image restoration) and to reduce image data sizes for storage or transmission (image compression). These techniques are valuable in a range of applications and careers including, but not limited to, medical imaging, astronomy, remote sensing, automation etc. Stress is placed on deep understanding of the principles underlying the techniques rather than memory learning of algorithms.

• Visualise via means of mental images the process of forming 1D and 2D Fourier transforms and also the convolution process. Describe the similarities and differences between the continuous and discrete Fourier transforms and their inter-relationship.
• Select and apply appropriate image enhancement methods for different applications. Discriminate between cases where automated image enhancement methods produce appropriate results and where they do not.
• Understand the differences between averaging and median filtering for reducing image noise.
• Demonstrate understanding of image smoothing and sharpening in both the image and Fourier domains. Select between optimum methods of edge detection in different applications.
• Describe common distorted images as convolutions of the true image with point spread functions (PSF). Describe and decide under which conditions different image restoration algorithms can be used and describe the strengths and weakness of these algorithms.
• Describe the Cosine transform and its relationship to the Fourier transform.
• Demonstrate a basic understanding of wavelets and know how to use them to compress and denoise data.
• Explain the difference between lossy and lossless compression methods and explain the concept of data redundancy as the source of compression. Describe the subcomponents of general compressor/decompressor algorithms. Calculate theoretical limits to lossless compression using the Shannon noiseless coding theorem and implement Huffman coding.
• Describe a variety of different mapping functions that can be used to obtain compression and decide when different methods are appropriate. Show via examples why Digital Pulse Code Modulation (DPCM) works and is stable in the face of quantisation errors.
• Describe the main components of the JPEG standard.
• Write computer code in MATLAB to implement selected image processing algorithms.

Introduction.  Image Enhancement: transform functions, and histogram
equalisation; image smoothing and sharpening; edge detection and noise
reduction; Fourier domain methods.  Continuous and Discrete 2D Fourier
Transforms.  Wavelets and Wavelet Applications.  Image Compression:
general compressor/decompressor, coding theorem, Huffman coding and
multi-pixel coding; run length coding, predictive coding and digital pulse
code modulation; cosine transform, block coding, zonal mask and threshold
mask; JPEG.  Image Restoration: linear space-invariant distortions, point
spread function, inverse and pseudoinverse filters; Wiener filter; image
reconstruction from projections.

Lectures, lab exercises, problem classes and project.

'Digital Image Processing' 3rd edition (2008) by Gonzalez and Woods.

Project and written exam.