Image Compression

1. Evolution of Image Processing Edward H. Land created the Retinex Theory 1971 1861 James clerk Maxwell Experimented with RGB to produce color photography 2000+ Scientist work to combine Retinex and RGB to make clear colored pictures Retinex Algorithms Images, both still and moving, are an integral part of our lives. We see images in newspapers, TV, internet, books, and magazines. NASA receives many images from various space telescopes, especially from Hubble space telescope. In this project, we studied how NASA processes and compresses images. Articles published by NASA’s Langley Center as well as other academic publications were reviewed. Once the research was completed the team developed a number and quantity unit for a New York State algebra course. Background Image Compression Abstract Image Processing Mathematically, any image can be represented as a vector where each pixel is a coordinate. The number value given to the pixel would be in respect to its color. An image with colors solely on the grayscale would typically have 262,144(512x512) pixels, or coordinates in the case of vectors, with values ranging from 0 to 255. A color image would have 3 times that amount due to the RGB(Red, Green Blue) color scale. Every color is the combination or absence of the Red, Green, and Blue. So, a color image represented as a vector, would have 786,432 coordinates. In terms of an image, that’s an immense amount of pixels. Compression reduces the amount of pixels. In images, pixels that are directly next to each other usually have like close values. Compression takes the similar values and simply addresses them as one pixel. There are different forms of compression that are performed using various bases, which is at the discretion of the agency and is based on what they are looking for and image. JPEG(Joint Photographic Expert Group) uses a Fourier Basis for their image compression. Images are typically in standard basis before compression, which mathematically is represented by a vector that is multiplied by a matrix with 1 in the component and 0 elsewhere. Unfortunately, that yields the same image with the same amount of data. Fourier basis(represented below) makes it so that coordinates reflect that two neighboring have close RBG values. It then collects all RGB values that are the same or are insignificantly different. This is typically performed in 8 by 8 blocks. Afterward, a threshold is determined. If a pixel value is within the selected threshold, it becomes a 0. This reduces the pictures data significantly. Sponsors and Contributors Retinex was designed to enhance an image that was transmitted either digitally or by analog. Using a series of algorithms Retinex enhances the contrast in specific areas of an image so that it is more visible. Below are some of the functions used, as well as an explanation, in the Retinex algorithm. NASA receives immense amounts of image data from satellites. The exorbitant amounts of data prove to be to difficult to be sent. The large amount of data from these images also are take up a lot of memory in storage space. Storage space is not infinite . Following the compression of an image, transmission and storage become much easier to do. The data size decreases which saves room on memory. The Hubble Telescope, for example, send pictures everyday and downlinks about 120 GB(Gigabytes) of data every week to the GSFC(Goddard Space Flight Center). That amount of data coming in on a consistent basis would encompass the storage space in short time. Compression makes it possible to save and later to send. The same rules apply to video data. The Curiosity(Mars Rover) can send about 2 million bits per second to the Mars Reconnaissance Orbiter. That extreme amount of data must be compressed for transmission and storage. A number of images are received with a lack of color or missing important elements, (such as hydrogen atoms, oxygen atoms, and nitrogen ions). There are two forms of image processing to improve an image. First is Color Addition but more importantly is Retinex, both forms are used to bring out what may not be seen in an image by the human eye. Image Compression and Image Processing Image compression is a mathematical process of eliminating data that may be irrelevant or redundant in an image. The redundancies are then compiled. At the end of the process the data amount of the image decreases significantly allowing for easier transmission and storing. Conclusion and Future Work The current administration has put a lot of focus on Science Technology Engineer Mathematics (STEM) education. Educate to Innovate, a STEM education campaign, as well as a number of congressional acts have provided resources and attention to STEM careers and education. Additionally, national standards called the Common Core use specific language in what and how the American student is expected to learn. A typical STEM education under the Common Core requires stronger literacy skills, evidence of problem solving on the part of the student, and the ability to explain cognitive steps taken. The research summer experience at Hostos Community College in affiliation with NASA GISS provided a new model of STEM education to the participants. Alyssa Taylor, the high school rising Senior, was responsible to learn the material needed to discuss and understand image processing and compression. She had frequent check ins with her professor but had to read and practice the material on her own. Any misconceptions she had would be clarified by the professor during a check in but Alyssa was responsible for her own learning. This model inspired the team to come up with a math curriculum that involved NASA image processing but also put more responsibility on the student. Through further research the team found out about a movement in education called Flipped Instruction. Professor Tanvir Prince was a flipped instructor. While he did lecture from time to time it was only after he checked in with the rest of the team when he would decide to teach a lesson or not. Sometimes he deemed a lesson unnecessary because the readings and the videos sufficed the learning objectives. Feeling that this type of learning experience is inline with current STEM education goals the team decided to build and measure a “flipped” Numbers and Quantity unit with a focus on NASA image processing. This unit would follow the current expectations of a STEM course: strong literacy component, problem solving activities and opportunities to explain steps taken. The unit would be taught in a 9th grade integrated algebra class. The effectiveness of the course would be measured by gains in literacy skills, New York State Regent test scores and surveys on interest in STEM professions. RetinexColor Addition Graphic Example • Multiscale retinex with Color Restoration (MSRCR) • The use of an image enhancement algorithm that simultaneously produces a compressed, color constant, sharper image. • The main purpose of retinex is to enhance parts of an image that has poor contrast /lightness but not to disturb the parts that have good quality. As shown below. For this image the inferred light was used to make the image more visible. There are three wave lengths, each assigned to a color. (blue to the shortest. red to the longest. green to the intermediate). Compression Matrices This image is an example of using different filters of light. 8x8 block in the standard basis 8x8 block after JPEG compression Sponsors: National Aeronautics and Space Administration (NASA) NASA Goddard Space Flight Center (GSFC) NASA Goddard Institute for Space Studies (GISS) CUNY Hostos CC & City Tech USDE NSF Contributors: Prof. Tanvir Prince (Mentor) Noam Pillischer (HS Teacher) Maurice J. Evans (UG Student) Alyssa Taylor (HS Student) Special Thanks: CILES Director Dr. Jorge Gonzales CILES Mentor Dr. Nieves Angulo R is retinx output. X is the pixel location. The sub-index I represents the ith spectral band, N is the number of bands W is the weight associated, Rkis the single scale retinex defined by the second equation.