Furthermore, we propose an adaptive anisotropy factor of which the value decreases as the kernel scale increases. This factor improves the noise robustness of small-scale kernels while alleviating the anisotropy stretch effect that occurs in conventional anisotropic methods. Finally, we evaluate our ...
A simple necessary and sufficient condition,on a trace-class kernel K,is given in order for the existence of a measurable (relative to the complete product sigma-algebra) Gaussian process with covariance K. The integral of the exponential of a certain function of a Gaussian process with respect...
This is done by a weighted average using a Gaussian kernel. Using the described process, each particle moves with the average velocity of its neighborhood, resembling the collective velocity of a group of people in the crowd. Given the averaged velocity components that move each particle, e.g....
A Gaussian measure is logarithmically differentiable exactly in the directions of its Cameron–Martin space and the derivatives may be found explicitly. For these measures, the above results form just a beginning of the story; see, for example, [8] for much more. The natural problem of unique...
A family of kernels is derived that constitute discrete analogues to the continuous Gaussian derivatives.The representation has theoretical advantages over other discretizations of the scale-space theory in the sense that operators that commute before discretization commute after discretization. Some ...
The bound depends on functionals and the Gaussian hypergeometric function, but it is of rather simple form. The Peano-Sard theorem is still very unexplored in fractional calculus. As this paper demonstrates, it has a great potential to derive new inequalities that generalize the ordinary ones. ...
Furthermore, we propose an adaptive anisotropy factor of which the value decreases as the kernel scale increases. This factor improves the noise robustness of small-scale kernels while alleviating the anisotropy stretch effect that occurs in conventional anisotropic methods. Finally, we evaluate our ...
Mapping the change of intensities is typically achieved through the convo-lution of the image with some function kernel, a step edge operator . Canny[2] concerned himself with the derivation of an optimal step edge operator;he found that a first-derivative Gaussian function closely approximates ...
However, in the Rouse model, the step length of this random walk is Gaussian distributed (i.e., in three dimensions P(r) ∼ r2exp(−3r2/(2b2)), whereas in the freely jointed case the distribution is narrow with the average length r0. All other models have increasing d(s), ...
We focus in this paper on the derivative sampling reconstruction, where the reconstruction procedure utilizes samples of both the signal and its first derivative. Our major aim was to incorporate the reconstruction sampling operator with a Gaussian regularization kernel, which on the one hand is ...