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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]
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Image derivatives can be computed by using small convolution filters of size 2 × 2 or 3 × 3, such as the Laplacian, Sobel, Roberts and Prewitt operators. [1] However, a larger mask will generally give a better approximation of the derivative and examples of such filters are Gaussian derivatives [ 2 ] and Gabor filters . [ 3 ]
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 ...
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 name raster graphics editor is sometimes used to contrast this approach to that of general editors which also handle vector graphics. One of the first popular image editors was Apple's MacPaint, companion to MacDraw. Modern examples are the free GIMP editor, and the commercial products Photoshop and Paint Shop Pro.
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