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papers:simard-99 [2006/12/13 12:07] leonb |
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- | ===== Boxlets: a fast convolution algorithm | + | ===== Boxlets: a Fast Convolution Algorithm |
+ | |||
+ | // | ||
+ | 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, | ||
+ | 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. | ||
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} | } | ||
+ | |||
+ | ==== 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. This was also described in [3] (see the paper for details.) | ||
+ | |||
+ | |||
+ | * **[1]** | ||
+ | * **[2]** Paul Viola, Michael Jones: Robust Real-time Object Detection, // | ||
+ | * **[3]** Paul S. Heckberg: | ||
+ | conference on Computer graphics//, 20:315-321, Dallas, 1986 |