1 / 24

Math 3360: Mathematical Imaging

Math 3360: Mathematical Imaging. Lecture 1: Introduction to mathematical image processing. Prof. Ronald Lok Ming Lui Department of Mathematics, The Chinese University of Hong Kong. Lecturer: Prof. Ronald Lui Email: lmlui@math.cuhk.edu.hk Tel: 3943-7975

williamlross
Download Presentation

Math 3360: Mathematical Imaging

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Math 3360: Mathematical Imaging Lecture 1: Introduction to mathematical image processing Prof. Ronald Lok Ming LuiDepartment of Mathematics, The Chinese University of Hong Kong

  2. Lecturer: Prof. Ronald Lui • Email: lmlui@math.cuhk.edu.hk • Tel: 3943-7975 • Office: Lady Shaw Building (LSB) 207 • Lecture time (?): Mon 8:30am-10:15am; Fri 9:30am-10:15am (How about: Mon 8:45am-10:15am?) • Textbook: Will be based on ppt, lecture notes uploaded on the course website • Course website: http://www.math.cuhk.edu.hk/~lmlui/Math3360.html • Other references: • Image processing: the fundamentals by Maria Petrou and Costas Petrou [Free access of online version on CUHK library] • Fundamentals of Digital Image Processing: A Practical Approach with Examples in Matlab by Chris Solomon and Toby Breckon [Free access of online version on CUHK library] • Digital Image Processing (3rd ed.) by Rafael C. Gonzalez and Richard E. Woods [Available in CUHK bookstore] Some Useful Information

  3. Assessment scheme: • Homework assignment (written and programming) 15% [Programming homeworks will only require basic Matlab programming skills. The usage of Matlab will also be discussed as they are used. The aim is to let students appreciate and enjoy the importance of mathematics in imaging through actual (simple) implementation.] • Midterm   35% • Final   50% • Midterm + Final will be based on homework + pool of practice exercises • Incline to give good grades to as many students as possible! • Relax + enjoy + arouse interest in imaging! • Good students should be able to work on a research project on imaging with me (if interested). Some Useful Information

  4. Mathematical + Image Processing What is our goal in Math 3360? IMAGE PROCESSING TASKS: Denoising, Segmentation, Registration, Compression,… MATHEMATICS: Linear algebra, Calculus, transformation,…

  5. Topic to be covered: • Introduction to digital images and imaging geometry; • Image transformations: DFT, DST, SVD etc; • Image compression; • Statistical description of images; • Image enhancement and Image restoration; • Image segmentation and edge detection What is our goal in Math 3360?

  6. Image denoising: • Image can be corrupted by “noises” during transmission or error during capturing the image intensity • Reconstruct a “clean” (usually visually) image from the noisy one Some tastes about IMAGING

  7. Image denoising: • Where is the MATHEMATICS? • Minimization model: • Solving PDE: Some tastes about IMAGING Don’t worry about the mathematics! You will learn it (simple version) and find it easy later!

  8. Image segmentation: • Image may contain too much information. • Need: extract useful information from an image. • Image segmentation aims to automatically extract important part or regions of an image. Some tastes about IMAGING

  9. Image segmentation: • Where is the Mathematics? • Minimization model: Some tastes about IMAGING Don’t worry about the mathematics! You *may* learn it (simple version)!

  10. Image compression: • Image compression aims to use less storage to represent an image. • Do you know familiar JPEG compression is actually based on mathematical theories? You will learn how it works in Math 3360. Some tastes about IMAGING

  11. Mathematical definition: • A 2D (grayscale) digital image is a 2D function defined on a 2D domain (usually rectangular domain): • is called the brightness/intensity/grey level; • (x,y) is the spatial coordinates of the image. • Thus, a 2D digital image looks like this: • Each element in the matrix is called pixel (picture element); • Usually, and What is a digital image? IMAGE PROCESSING IS RELATED TO LINEAR ALGEBRA!!

  12. Mathematical definition of color image: • A 2D (color) digital image is a 2D function defined on a 2D domain (usually rectangular domain): • are the intensity/brightness/grey level corresponding to R, G and B respectively ; • Combination of R, G, B forms the full spectrum of color! What is a digital image? WE WILL FOCUS ON: Grayscale image!

  13. Sensor: • Each sensor captured the amount of photon of certain wavelength; • Typical color images consist of three color bands (RGB). • Reflected light of an object/phontons are captured by three different sets of sensors, each set made to have a different sensitivity function. How is a digital image formed? Figure 1: The spectrum of the light which reaches a sensor is multiplied with the sensitivity function of the sensor and recorded by the sensor. This recorded value is the brightness ofthe image in the location of the sensor and in the band of the sensor. This figure shows thesensitivity curves of three different sensor types.

  14. Example 1: • A digital camera has a triple array of 3x3 sensors: • The wavelengths of the photons that reach the pixel locations of each triple sensor: • Sensitivity of the sensor: How is a digital image formed?

  15. Example 1.1: (Continued) • Intensity: How is a digital image formed?

  16. Image resolution: • Recall: A digital image looks like: where: • (N,G) is called the image resolution. • Sometimes, (n,m) is referred to as image resolution as well. What is “Image resolution”?

  17. Example 1.2: (Convert an image to the prescribed digital band) • Divide the range of value into 8 bands: • We get: Image resolution rescaling

  18. Effect on different image resolution: • Checkerboard effect: reducing N What is “Image resolution”?

  19. Effect on different image resolution: • False contouring: reducing M What is “Image resolution”?

  20. Little Effect by m on a complicated image: What is “Image resolution”?

  21. Good image contrast means: • grey values present in the image range from black to white; • making use of the full range of brightness to which the human vision system is sensitive. What is “Image contrast”?

  22. Normalization to get good image contrast • Example 1.3: • Measured intensity: • Divide according to the min and max of intensity: What is “Image contrast”?

  23. Normalization to get good image contrast • Example 1.3: • Final result after normalization: • Compare with: What is “Image contrast”?

  24. Keep in mind: imread & imwrite! • Please attend TA session when you will learn MATLAB command to do mathematical imaging! How do we read a digital image in Matlab?

More Related