![]() These are some of the shortcomings of Huffman encoding which are addressed by arithmetic coding to be discussed later. That is, we need block codes of large sizes. While in some other cases, such as sources with few symbols and skewed probabilities of symbols, the improvement is not immediate. This extension of the source can provide dramatic improvements in coding efficiency in some cases. In the latter case, groups of symbols are combined, to form a new symbol, generated by the so called extended source, with an increased alphabet size. In this segment, we show the methodology for designing first order, as well as block Huffman codes. It provides a straightforward methodology based on the Morse principle for designing a prefix and therefore, a uniquely decodable code. The most celebrated variable length code was derived in 1951 by David Huffman, and it carries his name. In all cases, example images and videos pertaining to specific application domains will be utilized. Emphasis on the special role sparsity plays in modern image and video processing will also be given. We will introduce and use a wide variety of such tools – from optimization toolboxes to statistical techniques. In this class not only will you learn the theory behind fundamental processing tasks including image/video enhancement, recovery, and compression - but you will also learn how to perform these key processing tasks in practice using state-of-the-art techniques and tools. We will provide a mathematical framework to describe and analyze images and videos as two- and three-dimensional signals in the spatial, spatio-temporal, and frequency domains. This course will cover the fundamentals of image and video processing. Some important examples of image and video processing include the removal of degradations images suffer during acquisition (e.g., removing blur from a picture of a fast moving car), and the compression and transmission of images and videos (if you watch videos online, or share photos via a social media website, you use this everyday!), for economical storage and efficient transmission. Digital image and video processing continues to enable the multimedia technology revolution we are experiencing today. The ability to process image and video signals is therefore an incredibly important skill to master for engineering/science students, software developers, and practicing scientists. Moreover they come in a wide range of the electromagnetic spectrum - from visible light and infrared to gamma rays and beyond. In this class you will learn the basic principles and tools used to process images and videos, and how to apply them in solving practical problems of commercial and scientific interests.ĭigital images and videos are everywhere these days – in thousands of scientific (e.g., astronomical, bio-medical), consumer, industrial, and artistic applications. An example set of probabilities to reach the maximum is. ![]() So 2/5–ϵ, where ϵ is the smallest number that allows the probability computed from the frequency, presumably an integer, to be less than 2/5. ![]() The rest is left as an exercise for the reader. So p(D) must be strictly less than p(A) + p(B). Note that if p(C) = p(D) = p(A) + p(B), then the Huffman algorithm has the option to pick any pair in the next step, for which two of those cases results in skewed tree. To assure that we combine C and D into a branch, p(C) and p(D) must both be less than p(A) + p(B). Then the final step will be to combine those two branches. (Again, without loss of generality if some of the probabilities are equal.) In order for the resulting tree to be flat, we must then combine C and D into a branch. ![]() The Huffman algorithm will combine A and B into a branch. Without loss of generality, we will assume that p(A) <= p(B) <= p(C) <= p(D). ![]()
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