S. Mandayam/ DIP/ECE Dept./Rowan University Digital Image Processing ECE /ECE Fall 2007 Shreekanth Mandayam ECE Department Rowan University Lecture 8 November 12, 2007

S. Mandayam/ DIP/ECE Dept./Rowan University Plan Digital Image Compression Fundamental principles Image Compression Model Recall: Information Theory Image Compression Standards DCT (JPEG): Lossy LZW (GIF, TIFF, ZIP): Lossless Lab 3: Digital Image Restoration Lab 4: Digital Image Compression Discussion: Final Project

S. Mandayam/ DIP/ECE Dept./Rowan University DIP: Details

S. Mandayam/ DIP/ECE Dept./Rowan University Fundamentals Justification Applications Principle Redundancy Types Lossy Lossless demos/demo6dithering/

S. Mandayam/ DIP/ECE Dept./Rowan University Compression Model f(x,y) Transform Quantize Encode Source Channel

S. Mandayam/ DIP/ECE Dept./Rowan University Recall: Measures of Information Definitions Probability Information Entropy Source Rate Recall: Shannon’s Theorem If R < C = B log 2 (1 + S/N), then we can have error- free transmission in the presence of noise MATLAB DEMO: /ecomms/entropy.m

S. Mandayam/ DIP/ECE Dept./Rowan University Recall: Source Encoding Why are we doing this? Analog Message A/D Converter Digital Source Encoder Source Symbols (0/1) Source Entropy Encoded Symbols (0/1) Source-Coded Symbol Entropy

S. Mandayam/ DIP/ECE Dept./Rowan University Source Encoding Requirements Decrease L av Unique decoding Instantaneous decoding

S. Mandayam/ DIP/ECE Dept./Rowan University Recall: Huffman Coding 2-Step Process Reduction List symbols in descending order of probability Reduce the two least probable symbols into one symbol equal to their combined probability Reorder in descending order of probability at each stage Repeat until only two symbols remain Splitting Assign 0 and 1 to the final two symbols remaining and work backwards Expand code at each split by appending a 0 or 1 to each code word Example m(j)ABCDEFGH P(j)

S. Mandayam/ DIP/ECE Dept./Rowan University Discrete Cosine Transform Information Concentration Data Compaction Feature Extraction Discrete Cosine Transform >>dctdemo

S. Mandayam/ DIP/ECE Dept./Rowan University Laser Based Ultrasound* *Karta Technologies Inc., San Antonio, TX

S. Mandayam/ DIP/ECE Dept./Rowan University Example: Photothermal Shearography Images Before Deformation - After Deformation = Fringe Pattern Sample mm depth MPa stress

S. Mandayam/ DIP/ECE Dept./Rowan University Preprocessing Fringe Pattern DCT DCT Coefficients Zonal Mask (1,1) (1,2) (2,1) (2,2). Feature Vector Artificial Neural Network

S. Mandayam/ DIP/ECE Dept./Rowan University JPEG Compression Standard f(x,y) Level Shift Compute DCT F(u,v) Normalize Reorder to form 1-D Sequence Compute DC Coefficient Compute AC Coefficients

S. Mandayam/ DIP/ECE Dept./Rowan University LZW Algorithm Initialize string table with single character strings Read first input character = w Read next input character = k No more k’s? Output = code(w) Stop wk in string table? Output = code(w) w = wk w = k Put wk in string table y n n y United States Patent No. 4,558,302, Patented by Unisys Corp.

S. Mandayam/ DIP/ECE Dept./Rowan University Karhunen-Loeve (Hotelling) Transform Hotelling transform of x demos/demo7klt/

S. Mandayam/ DIP/ECE Dept./Rowan University Lab 3: Digital Image Restoration

S. Mandayam/ DIP/ECE Dept./Rowan University Lab 4: Digital Image Compression

S. Mandayam/ DIP/ECE Dept./Rowan University Final Project

S. Mandayam/ DIP/ECE Dept./Rowan UniversitySummary