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2D convolution with an M × N kernel requires M × N multiplications for each sample (pixel). If the kernel is separable, then the computation can be reduced to M + N multiplications. Using separable convolutions can significantly decrease the computation by doing 1D convolution twice instead of one 2D convolution. [2]
This ensures that a two-dimensional convolution will be able to be performed by a one-dimensional convolution operator as the 2D filter has been unwound to a 1D filter with gaps of zeroes separating the filter coefficients. One-Dimensional Filtering Strip after being Unwound. Assuming that some-low pass two-dimensional filter was used, such as:
The use of Richardson–Lucy deconvolution to recover a signal blurred by an impulse response function. The Richardson–Lucy algorithm, also known as Lucy–Richardson deconvolution, is an iterative procedure for recovering an underlying image that has been blurred by a known point spread function.
Its impulse response is defined by a sinusoidal wave (a plane wave for 2D Gabor filters) multiplied by a Gaussian function. [6] Because of the multiplication-convolution property (Convolution theorem), the Fourier transform of a Gabor filter's impulse response is the convolution of the Fourier transform of the harmonic function (sinusoidal function) and the Fourier transform of the Gaussian ...
The spreadsheets, as well as graphs and note windows, are gathered in a project and can be organized using folders. The built-in analysis operations include column/row statistics, (de)convolution, FFT and FFT-based filters.
The design of an N-dimensional window particularly a 2-D window finds applications in various fields such as spectral estimation of multidimensional signals, design of circularly symmetric and quadrantally symmetric non-recursive 2D filters, [1] design of optimal convolution functions, image enhancement so as to reduce the effects of data ...
The Hough transform [3] can be used to detect lines and the output is a parametric description of the lines in an image, for example ρ = r cos(θ) + c sin(θ). [1] If there is a line in a row and column based image space, it can be defined ρ, the distance from the origin to the line along a perpendicular to the line, and θ, the angle of the perpendicular projection from the origin to the ...
GNU Octave is a scientific programming language for scientific computing and numerical computation.Octave helps in solving linear and nonlinear problems numerically, and for performing other numerical experiments using a language that is mostly compatible with MATLAB.
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