Main presenter			Co-presenter(s)
Name :	Dr. Mark Michael		Name:
E-mail:	mmichael@acm.org		E-mail:
Institution or Company:	King's College (Pennsylvania)		Name:
Department:	Computer Science		E-mail:
City:	Wilkes-Barre		Name:
State/Province:	PA		E-mail:
Country:	USA		Name:
Type of presentation:	Lecture :  25 minutes.		E-mail:
Conference strand and number:	Derive & TI-CAS  ,    Number: D20		Schedule:   Room:	Saturday, 15h00   1350
Related website:
Title of presentation:	Using Derive to Explore the Mathematics of the JPEG Image Compression Algorithm
Abstract:
Many photographic images displayed on Web pages and saved on CDs have been compressed via an algorithm developed by the Joint Photographic Experts Group (JPEG). The algorithm employs several mathematical techniques, but at its heart is the application of the Discrete Cosine Transform (DCT) -- a variant of the classic Fourier Transform -- to 8x8 blocks of pixels. While standard graphics programs can be used to compare the image degradation corresponding to different, vaguely defined levels of compression, Derive allows one to choose precise values for numerous algorithm parameters and to examine in detail what takes place at each step in the process. Insight into frequency-space representations of data can be gained by generating "test images" (8x8 matrices) with various properties to see how the crucial DCT expresses regularity and diversity. Preceding the DCT step are an obligatory transformation from red-green-blue color-coordinates to luminance-chrominance coordinates and an optional downsampling (loss of chrominance information). Following the DCT step is a quantization step, which allows the customization of the way information (especially "high frequency" data) is discarded. Even a "lossless" step may contribute round-off error; this can be investigated by running the step and its inverse with different numbers of digits of precision. Derive makes it possible to automate investigations by perfoming one or more steps with multiple choices for images or parameters via a single simplification command.