## Boxlets: a Fast Convolution Algorithm for Neural Networks and Signal Processing

Abstract: Signal processing and pattern recognition algorithms make extensive use of convolution. In many cases, computational accuracy is not as important as computational speed. In feature extraction, for instance, the features of interest in a signal are usually quite distorted. This form of noise justifies some level of quantization in order to achieve faster feature extraction. Our approach consists of approximating regions of the signal with low degree polynomials, and then differentiating the resulting signals in order to obtain impulse functions (or derivatives of impulse functions). With this representation, convolution becomes extremely simple and can be implemented quite effectively. The true convolution can be recov- ered by integrating the result of the convolution. This method yields substantial speed up in feature extraction and is applicable to convolutional neural networks.

Patrice Simard, Léon Bottou , Patrick Haffner and Yann Le Cun: Boxlets: a fast convolution algorithm for neural networks and signal processing, Advances in Neural Information Processing Systems 11 (NIPS 1998), 571-577, MIT Press, Denver, 1999.
@incollection{simard-99,
author = {Simard, Patrice and Bottou , L\'{e}on and Haffner, Patrick and  {LeCun}, Yann},
title = {Boxlets: a fast convolution algorithm for neural networks and signal processing},
booktitle = {Advances in Neural Information Processing Systems 11 (NIPS 1998)},
publisher = {MIT Press},
year = {1999},
pages = {571--577},
url = {http://leon.bottou.org/papers/simard-99},
}

### Notes

Maybe the most famous use of boxlets is the computation of the features of the Viola-Jones object recognition system [1,2]. The integral image representation is a boxlet of order zero. Such particular cases were also described in [3] (see the paper for details.)

• [1] Paul Viola, Michael Jones: Robust Real-time Object Detection, Second International Workshop on Statistical and Computational Theories of Vision - Modeling, Learning, Computing, and Sampling, Vancouver, July 2001.
• [2] Paul Viola, Michael Jones: Robust Real-time Object Detection, International Journal of Computer Vision, 57(2):137-154, 2004
• [3] Paul S. Heckberg: Filtering by repeated integration. ACM SlGGRAPH conference on Computer graphics, 20:315-321, Dallas, 1986
papers/simard-99.txt · Last modified: 2018/12/06 10:04 by leonb