the integral of the velocity," said Melkana Brakalova-Trevithick, chair of the math department at Fordham University, who chose this equation as her favorite. "The fundamental theorem of calculus (FTC) allows us to determine the net change over an interval based on the rate of change over ...
Note that the linear motion of an object can be described by the traveling wave equation. This model may be used for explaining the formation of the above image blur and for its restoration in spatial domain as well. Investigations in this paper are first made on the removal of image blur...
This equation was originally investigated in 2D in the 18th century. However, today, using modern computer graphics techniques, full 3D versions can be visualized. The geometrical surfaces of the rose functions correspond to the zeros of the equations and are visualized as the isosurfaces of 3D ...
Then we multiply the result by a scale parameter β and perform an element-wise sum operation with A to obtain the final output EE∈ RC×H×W: Ej=β∑i=1C(xjiAi)+Aj (3) where β gradually learns a weight from 0. Equation 3 shows that the final feature of each channel is a ...
Among the whole set of hyper-parameters that may impact the performance of the StyleGAN2, the target heuristic [Math Processing Error]rt (see Equation 4 in Methods) depends on the dataset, as mentioned in Karras et al.8, and deserves to be tuned in the present study. To this end, we ...
It is faster to proofread an automated reconstruction generated via convolutional nets7. However, automated reconstruction depends on the preceding step of aligning the 2D section images into a 3D image stack. Misalignments can be the dominant cause of errors in the automated reconstructions, so it ...
An application that maps an image of a LaTeX math equation to LaTeX code. Introduction The problem of image-to-markup generation was attempted byDeng et al. (2016). They extracted about 100K formulas by parsing LaTeX sources of papers from the arXiv. They rendered the formulas using pdflatex...
Towards a Four-dimensional Model of the country image To develop an integrative model of the country image we draw on three basic concepts: the concept of national identity by Smith (1991) to substantiate generic attributes of the reference object of the country; the attitude theory by Ajzen an...
Noise removal using fourth-order partial differential equation with applications to medical magnetic resonance images in space and time In this paper, we introduce a new method for image smoothing based on a fourth-order PDE model. The method is tested on a broad range of real medical magne.....
This gives an enormous reduction of storage space and computation, because \({\tilde{S}}\otimes S'\) is not computed at all. The equation \(Y = SX{\tilde{S}}'\) can be interpreted as \(Y = (S X){\tilde{S}}'\), or as first convolving the columns of X with S, followed...