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| - | ===== Boxlets: a fast convolution algorithm | + | ===== Boxlets: a Fast Convolution Algorithm |
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| + | // | ||
| + | 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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| } | } | ||
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| + | ==== Notes ==== | ||
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| + | Maybe the most famous use of boxlets is the computation of the features of the Viola-Jones face detector [1]. The //integral image// representation is a boxlet of order zero. This was also described in [2] (see the paper for details.) | ||
| + | |||
| + | * **[1]** Paul Viola, Michael Jones: Robust Real-time Object Detection, // | ||
| + | * **[2]** Paul S. Heckberg: | ||
| + | conference on Computer graphics//, 20:315-321, Dallas, 1986 | ||