New Concepts in Image And Video Processing Utilizing Distributed Computing Dr. Chance M. Glenn, Sr. Associate Professor – ECTET Department Director – The McGowan Center for Telecommunications, Innovation and Collaborative Research Rochester Institute of Technology Research Computing Seminar Series

Content I.Introduction II.Background – Chaotic Dynamics III.The D-Transform Algorithm IV.Applications V.Fourier Series Waveform Classification VI.Results VII.Cluster Usage VIII.Acknowledgements Research Computing Seminar Series

Communication Technology and Networking Demands continue to increase Bandwidth Throughput Processing time (real-time applications) Convergence Digital Rights Management Efficient use of bandwidth Modulation Compression Network efficiency I. Introduction Research Computing Seminar Series

where Circuit diagram: A typical chaotic oscillator is the Colpitts system. The Colpitts circuit is a typical circuit topology used in the engineering design of oscillators. Equations of motion: II. Background – Chaotic Dynamics Research Computing Seminar Series

II. Background – Chaotic Dynamics Research Computing Seminar Series

Time-dependent waveforms Note the waveform variation in these segments Initial conditions Smoothly varying waveforms II. Background – Chaotic Dynamics Research Computing Seminar Series

II. Background – Chaotic Dynamics Equations of motion: (a) Another chaotic system - Lorenz Research Computing Seminar Series

II. Background – Chaotic Dynamics (a) Suppose we have multiple chaotic oscillators, where each one may be multi- dimensional systems: s 1, s 2, s 3, …, s M Each oscillation component can be described as: s m (n,x), where n is the component number. The z component of the Lorenz oscillation above may be described as: s 2 (3,x). We generated new sets of chaotic oscillations by combining these standard oscillations together to create more complex forms: c nT (x) = F[s 1 (1,x),…,s 1 (N,x),…,s M (1,x),…,s M (N,x)] where nT is a type number Research Computing Seminar Series

II. Background – Chaotic Dynamics (a) We’ve created a combined chaotic oscillation (CCO) matrix which is comprised of a set of 32 sequences, each holding 2 16 points of 16-bit resolution (4096 KB) c1(i)c1(i) c2(i)c2(i) c3(i)c3(i) c 32 (i) Our premise is that if we improve the metric entropy of the CCO set, then we increase the probability of matching arbitrary naturally varying waveforms Research Computing Seminar Series

III. The D-Transform Algorithm The D-transform takes advantage of the time diversity inherent in chaotic processes. CONCEPT: segments of a digital sequence, x, such as that derived from audio, video, and image data (and other data), can be replaced by the segments extracted from a CCO matrix that matches it within an acceptable error tolerance. Symbolically, we can describe the D-transform and inverse D- transform operators as: D C k d x D -1 C k d x’x’ Research Computing Seminar Series

is the original digital sequence, is the combined chaotic oscillation matrix (static), and is the matrix ordering sequence. where then compression occurs. We reproduce the digital sequence by The point-wise error between the original and reconstructed sequence is is the total error between the sequences. E = 0 mean lossless compression. if is the length function III. The D-Transform Algorithm DYNAMAC (DY-na-mac) stands for dynamics-based algorithmic compression. Research Computing Seminar Series

Digital Sequence Initialization file Sequence Parser C Combined Chaotic Oscillation Matrix (32x65536x16) CO Decimator Scaling Comparator Input Buffer x[n] xp[n] Ns c n [n]  [n] c[n] Nc ff D-bite generator Nt Ni Nc Fixed Storage Ns Ni Nt Nc Ns D = [D1,D2,D3,D4] BLOCK DIAGRAM (EXAMPLE) III. The D-Transform Algorithm DYNAMAC Implementation Research Computing Seminar Series

III. The D-Transform Algorithm from row 400 – 64 pixels (green)original image Ns = 64 Research Computing Seminar Series

III. The D-Transform Algorithm c = N s N b /N D compression ratio where, N s – length of data segment N b – bit resolution per channel N D – number of bits to represent d-bite ex. N s = 64, N b = 8, N D = 40 c = 12.8:1 Research Computing Seminar Series

III. The D-Transform Algorithm Original BMP image Decompressed DYN image Research Computing Seminar Series

IV. Applications Digital Rights Management Image scrambled with a 160-bit key Research Computing Seminar Series

IV. Applications Content Distribution D x kaka C d D -1 x2x2 kuku C x3x3 kaka C x4x4 kaka C xNxN kuku C … Simultaneous streaming of content to users on a network. Unauthorized users, signified with dots, will not receive quality content. D -1 kaka C x1x1 Digital Rights Management Research Computing Seminar Series

IV. Applications Biomedical Image Analysis Could be used to detect abnormalities and diseased tissue in digital images for early detection. Research Computing Seminar Series

IV. Applications Video Tracking/Surveillance Subject vehicle: Black Car Error: 0.23 Research Computing Seminar Series

IV. Applications Video Tracking/Surveillance Subject vehicle: Black Car 6 seconds later error: 0.12 Research Computing Seminar Series

V. FSWC Fourier Series Waveform Classification c1(i)c1(i) c2(i)c2(i) c3(i)c3(i) c 32 (i) CHALLENGE: In order to extract oscillations from the CCO matrix, we slide a window of length N c through each of the the 32 oscillation types. Each extracted oscillation is compared to the original. There will roughly be 2 16 extractions and comparisons Time consuming! (skip 32 points) Research Computing Seminar Series

V. FSWC Fourier Series Waveform Classification SOLUTION: If we can determine a method of waveform classification, we can group waveforms into families. Only similar families need be searched. Fourier Series Decomposition: Research Computing Seminar Series

V. FSWC Fourier Series Waveform Classification If we break the Fourier coefficient space into discrete partitions: We get the 18-bit sequence b = We have 3-bit resolution with 3 terms. We call this M-N FSWC (3-3 FSWC) b = b A1 b B1 b A2 b B2 b A3 b B3 Generates 2MN bits Families are subsets of b Research Computing Seminar Series

V. FSWC Fourier Series Waveform Classification We can pre-classify a CCO matrix and store the results. EXAMPLE: N c = 128 extracted from three sections of c 4 (i) Research Computing Seminar Series

V. FSWC Fourier Series Waveform Classification 10-bit family: bf = (568) Research Computing Seminar Series

V. FSWC Fourier Series Waveform Classification 10-bit family: bf = (310) Research Computing Seminar Series

V. FSWC Fourier Series Waveform Classification 10-bit family: bf = (457) Research Computing Seminar Series

V. FSWC Fourier Series Waveform Classification Research Computing Seminar Series

V. Results Audio Example 16-bit, sample/sec, single channel digital audio Extracted segment 3-3 FSWC classification code: b = bf = (1023) Research Computing Seminar Series

V. Results Audio Example Family 1023 only had 230 members Speed increase: 65536/230 = 285 times Error = The error obtained using the traditional approach is essentially the same. Research Computing Seminar Series

V. Results Error calculation 8-bit Families10-bit Families M = 350.2/ /1.9 M = 433.4/ /1.17 We found that increasing the bit resolution, M, of the FSWC procedure improved accuracy, but a reduction of the processing time improvement. The table shows processing time improvement and the error ratio for different resolutions and different family lengths. Error ratio: e r = e FSWC /e 0 Research Computing Seminar Series

VI. Optimization Research Computing Seminar Series Compressed image CCO waveform utilization histogram CCO Matrix 3 CCO Matrix 2 CCO Matrix 1

VI. Optimization Research Computing Seminar Series

VI. Optimization Research Computing Seminar Series

VI. Optimization Research Computing Seminar Series The IBM Cluster was used to: Make large optimization runs Compress content for video Do comparative studies for speed, quality, and efficiency Develop potential hardware implementations We learned to use it as we went.

VI. Conclusions and Future Work The D-transform provides a new method of analysis for digital sequences. The D-transform can be used for digital data compression, identification, digital rights management, streaming, etc. FSWC dramatically improves the process, making it more realizable as a part of other algorithms. Latency time is decreased, processing time is decreased. FSWC has implications for other fields (digital modulation, general classification). We are working to implement this complete algorithm in hardware. Utilize the cluster more efficiently Research Computing Seminar Series

References 1.C. M. Glenn, M. Eastman, and N. Curtis, “ Digital Rights Management and Streaming of Audio, Video, and Image Data Using a New Dynamical Systems Based Compression Algorithm”, IADAT Conference on Telecommunications and Computer Networks, Conference Proceedings, September C. M. Glenn, M. Eastman, and G. Paliwal, “A New Digital Image Compression Algorithm Based on Nonlinear Dynamical Systems”, IADAT International Conference on Multimedia, Image Processing and Computer Vision, Conference Proceedings, March C. M. Glenn and T. Rossi, “Implementation of a New Codec for Broadcast and Digital Rights Management of High Definition Television”, 4th Annual Conference on Telecommunications and Information Technology, Conference Proceedings, March C. M. Glenn, “Clinical Analysis of Biomedical Images Using a New Nonlinear Dynamical Systems Based Transformation”, Submitted to IEEE Transactions on Signal Processing, Edward Ott, Chaos in Dynamical Systems, Cambridge Univ. Press, Canada, 1993.Moon book on chaos. Research Computing Seminar Series

References 6. Martin J. Hasler, Electrical Circuits with Chaotic Behavior, Proceeding sof the IEEE, vol. 75, no. 8, August P. S. Lindsay, Period Doubling and Chaotic Behavior in a Driven Anharmonic Oscillator, Phys. Rev. Lett. 47, 1349 (November 1981). 8. S. Hayes, C. Grebogi, E. Ott, A. Mark, Phys. Rev. Lett. 73, 1781 (1994). 9. T. Matsumoto, L. O. Chua, M. Komuro, The Double Scroll, IEEE Trans. CAS-32, no. 8 (1985), L. Nunes de Castro and F. J. Von Zuben, Recent Developments in Biologically Inspired Computing, Idea Group Publishing, Richard E. Blahut, Principles and Practice of Information Theory, Addison-Wesley Publishing Company, New York, Research Computing Seminar Series