Complexity Analysis of Iterative Basis Transformations Applied to Event-Based Signals

This paper introduces an event-based methodology to perform arbitrary linear basis transformations that encompass a broad range of practically important signal transforms, such as the discrete Fourier transform (DFT) and the discrete wavelet transform (DWT). We present a complexity analysis of the proposed method, and show that the amount of required multiply-and-accumulate operations is reduced in comparison to frame-based method in natural video sequences, when the required temporal resolution is high enough. Experimental results on natural video sequences acquired by the asynchronous time-based neuromorphic image sensor (ATIS) are provided to support the feasibility of the method, and to illustrate the gain in computation resources.

[1]  Mihaela van der Schaar,et al.  Incremental Refinement of Computation for the Discrete Wavelet Transform , 2007, ICIP.

[2]  Bevan M. Baas,et al.  A low-power, high-performance, 1024-point FFT processor , 1999, IEEE J. Solid State Circuits.

[3]  Bernabé Linares-Barranco,et al.  Mapping from Frame-Driven to Frame-Free Event-Driven Vision Systems by Low-Rate Rate Coding and Coincidence Processing--Application to Feedforward ConvNets , 2013, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[4]  Misha Anne Mahowald,et al.  VLSI analogs of neuronal visual processing: a synthesis of form and function , 1992 .

[5]  Ryad Benosman,et al.  Asynchronous event‐based high speed vision for microparticle tracking , 2012 .

[6]  Tobi Delbrück,et al.  Asynchronous Event-Based Binocular Stereo Matching , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[7]  Yu-Wei Lin,et al.  A 1-GS/s FFT/IFFT processor for UWB applications , 2005, IEEE Journal of Solid-State Circuits.

[8]  Chiara Bartolozzi,et al.  Asynchronous frameless event-based optical flow , 2012, Neural Networks.

[9]  Nitish V. Thakor,et al.  HFirst: A Temporal Approach to Object Recognition , 2015, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[10]  Ryad Benosman,et al.  Event-based 3D reconstruction from neuromorphic retinas , 2013, Neural Networks.

[11]  Ralph Etienne-Cummings,et al.  Real Time Compressive Sensing Video Reconstruction in Hardware , 2012, IEEE Journal on Emerging and Selected Topics in Circuits and Systems.

[12]  Tobi Delbrück,et al.  A 128$\times$ 128 120 dB 15 $\mu$s Latency Asynchronous Temporal Contrast Vision Sensor , 2008, IEEE Journal of Solid-State Circuits.

[13]  J. Tukey,et al.  An algorithm for the machine calculation of complex Fourier series , 1965 .

[14]  W. Sweldens.  The Lifting Scheme: A Custom - Design Construction of Biorthogonal Wavelets "Industrial Mathematics , 1996 .

[15]  T. Poggio,et al.  Hierarchical models of object recognition in cortex , 1999, Nature Neuroscience.

[16]  I. Daubechies.  Ten Lectures on Wavelets , 1992 .

[17]  C. Mead,et al.  The silicon retina. , 1991, Scientific American.

[18]  Abbes Amira,et al.  FPGA implementations of fast Fourier transforms for real-time signal and image processing , 2005 .

[19]  Chiara Bartolozzi,et al.  An Asynchronous Neuromorphic Event-Driven Visual Part-Based Shape Tracking , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[20]  T. Delbruck,et al.  > Replace This Line with Your Paper Identification Number (double-click Here to Edit) < 1 , 2022 .

[21]  Daniel Matolin,et al.  A QVGA 143 dB Dynamic Range Frame-Free PWM Image Sensor With Lossless Pixel-Level Video Compression and Time-Domain CDS , 2011, IEEE Journal of Solid-State Circuits.

[22]  Ryad Benosman,et al.  Asynchronous Neuromorphic Event-Driven Image Filtering , 2014, Proceedings of the IEEE.

[23]  Christoph Sulzbachner,et al.  Event-Based Stereo Matching Approaches for Frameless Address Event Stereo Data , 2011, ISVC.

[24]  I. Daubechies,et al.  Factoring wavelet transforms into lifting steps , 1998 .

[25]  Stéphane Mallat,et al.  A Theory for Multiresolution Signal Decomposition: The Wavelet Representation , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[26]  Abbes Amira,et al.  FPGA implementations of fast fourier transforms for real-time signal and image processing , 2003, Proceedings. 2003 IEEE International Conference on Field-Programmable Technology (FPT) (IEEE Cat. No.03EX798).

[27]  Gert Cauwenberghs,et al.  Analog VLSI Processor Implementing the Continuous Wavelet Transform , 1995, NIPS.

[28]  Emmanuel J. Candès,et al.  Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information , 2004, IEEE Transactions on Information Theory.

[29]  John Wawrzynek,et al.  A multi-sender asynchronous extension to the AER protocol , 1995, Proceedings Sixteenth Conference on Advanced Research in VLSI.

[30]  Ryad Benosman,et al.  Asynchronous Event-Based 3 D Reconstruction From Neuromorphic Retinas , 2013 .

[31]  Ryad Benosman,et al.  Visual Tracking Using Neuromorphic Asynchronous Event-Based Cameras , 2015, Neural Computation.

[32]  Kwabena Boahen,et al.  Point-to-point connectivity between neuromorphic chips using address events , 2000 .

[33]  Jin Jiang,et al.  Time-frequency feature representation using energy concentration: An overview of recent advances , 2009, Digit. Signal Process..