| L. J. van Vliet, I. T. Young, and P. W. Verbeek, "Recursive Gaussian derivative filters," in Proc. ICPR '98, 1998, pp. 509--514. |
....For the equal weighting scheme such as those for mean and variance calculation, only two operations are necessary for each pixel on each dimension of the input image. For a relatively fast Gaussian smoothing algorithm, it will need six operations for each pixel on each dimension of the input image [19]. The non linear min max operations, which are the fundamental mathematical morphology operations, need three operations for each pixel on each dimension of the input image [20] Fast Algorithm for nD Images We will now extend the 2D box filtering technique described in the previous section into ....
Vliet, L.J.V., Young, I.T. & Verbeek P.W. (1998) Recursive Gaussian derivative filters. In Proceedings of International Conference on Pattern Recognition, volume I, Brisbane, Australia, 16--20 August 1998. IEEE Computer, Society, pp. 509--514.
....a filtered version I G (x) of an image I(x) a discrete convolution with a kernel G is performed. Two dimensional convolutions with Gaussians and their derivatives can be computed very e#ciently because the kernels are separable, and highly accurate and e#cient recursive approximations exist [127]. Unfortunately, this is not generally true of rotated derivatives (Equation 3.3) Gaussian G 0 First derivative G Second derivative G # 3 2# 3 2 Figure 3.2. Visualization of a two dimensional Gaussian function and some oriented derivatives (cf. Equation 3.3) Zero values are shown ....
van Vliet, L. J., Young, I. T., and Verbeek, P. W. Recursive Gaussian derivative filters. In Proc. 14th International Conference on Pattern Recognition (ICPR'98) (Brisbane, Australia, Aug. 1998), vol. 1, IEEE Computer Society Press, pp. 509--514.
....Thus, a # = 1 kernel filter can be computed by two convolutions with the kernel [1, 2, 1] at a cost of two multiplications and 4 additions per pixel. 4.1. 3 Recursive filters Di#erent recursive implementations of Gaussian filters have been proposed by Deriche [5] and by Vliet, Young and Verbeek [13]. To maintain shift invariance (or zero phase) the filter is implemented as a cascade of forward and backward di#erence equations with real valued coe#cients b. Backward: v[n] #x[n] b i v[n i] Forward: y[n] #v[n] b i y[n i] with # = 1 i=1 b i . An interesting property ....
L. J. van Vliet, I. T. Young, and P. W. Verbeek. Recursive Gaussian derivative filters. In Proc. 14th International Conference on Pattern Recognition (ICPR'98), volume 1, pages 509-- 514. IEEE Computer Society Press, Aug. 1998.
....function, instantiated for convolution with a Gaussian kernel. The result is obtained by making the polynomial combination of different derivative filter responses, as given by the considered invariant. Gaussian filtering is implemented by using Infinite Impulse Response (IIR) filters described in [10]. Image similarity is calculated by considering feature histogram matching between the query image and the target image from the database. The feature histogram is derived from the color invariant chosen by the user. The k nearest neighbors are returned and ranked by their similarity with the ....
L. J. van Vliet, I. T. Young, and P. W. Verbeek. Recursive Gaussian derivative filters. In Proceedings ICPR '98, pages 509--514. IEEE Computer Society Press, 1998. 2
....a er = 1 kernel filter can be computed by two convolutions with the kernel [1, 2, 1] at a cost of two multiplications and 4 additions per pixel. 4.1. 3 Recursive filters Different recursive implementations of Gaussian fil ters have been proposed by Deriche [5] and by Vliet, Young and Verbeek [13]. To maintain shift invariance (or zero phase) the filter is implemented as a cascade of forward and backward difference equations with real valued coefficients. Backward: v[n] Forward: y[n] av[n] Z biy[n q i] with a = 1 i= bi. An interesting property of recursive filters is that the ....
L. J. van Vliet, I. T. Young, and P. W. Ver- beek. Recursive Gaussian derivative filters. In Proc. lth International Conference on Pattern Recognition (ICPR'98), volume 1, pages 509514. IEEE Computer Society Press, Aug. 1998.
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L.J. van Vliet, I.T. Young, and P.W. Verbeek, Recursive Gaussian Derivative Filters, Proc. 14th Int. Conference on Pattern Recognition, IEEE Computer Society Press, Los Alamitos, 1998, 509-514.
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L. J. van Vliet, I. T. Young, and P. W. Verbeek, "Recursive Gaussian derivative filters," in Proc. ICPR '98, 1998, pp. 509--514.
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