各種濾波處理總結

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	Filter Type 				Filters
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	<Linear Highpass>   Gradient, Laplacian
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	<Linear Lowpass> 			Smoothing, Gaussian
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	<Nonlinear Highpass> 		Gradient, Roberts, Sobel, Prewitt, Differentiation, Sigma
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	<Nonlinear Lowpass>			Median, Nth Order, Lowpass
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    Highpass filters emphasize significant variations of the light intensity usually found at the boundary of objects. Highpass frequency filters help isolate abruptly varying patterns that correspond to sharp edges, details, and noise.

    Lowpass filters attenuate variations of the light intensity. Lowpass frequency filters help emphasize gradually varying patterns such as objects and the background. They have the tendency to smooth images by eliminating details and blurring edges.

 Linear Filter:

 	If the filter kernel contains both negative and positive coefficients, the transfer function is equivalent to a weighted differentiation and produces a sharpening or highpass filter. Typical highpass filters include gradient and Laplacian filters.

	If all coefficients in the kernel are positive, the transfer function is equivalent to a weighted summation and produces a smoothing or lowpass filter. Typical lowpass filters include smoothing and Gaussian filters.

【Gradient Filter】
	
	A gradient filter highlights the variations of light intensity along a specific direction, which has the effect of outlining edges and revealing texture.

	The gradient filter has two effects, depending on whether the central coefficient x is equal to 1 or 0.

	If the central coefficient is null (x = 0), the gradient filter highlights the pixels where variations of light intensity occur along a direction specified by the configuration of the coefficients a, b, c, and d. The transformed image contains black-white borders at the original edges, and the shades of the overall patterns are darkened.

	If the central coefficient is equal to 1 (x = 1), the gradient filter detects the same variations as mentioned above, but superimposes them over the source image. The transformed image looks like the source image with edges highlighted. Use this type of kernel for grain extraction and perception of texture.

【Laplacian Filters】

	A Laplacian filter highlights the variation of the light intensity surrounding a pixel. The filter extracts the contour of objects and outlines details. Unlike the gradient filter, it is omnidirectional.

	If the central coefficient is equal to this sum x = 2(|a| + |b| + |c| + |d|), the Laplacian filter extracts the pixels where significant variations of light intensity are found. The presence of sharp edges, boundaries between objects, modification in the texture of a background, noise, or other effects can cause these variations. The transformed image contains white contours on a black background.

	If the central coefficient is greater than the sum of the outer coefficients (x > 2(a + b + c + d )), the Laplacian filter detects the same variations as mentioned above, but superimposes them over the source image. The transformed image looks like the source image, with all significant variations of the light intensity highlighted.

【Smoothing Filter】

	A smoothing filter attenuates the variations of light intensity in the neighborhood of a pixel. It smooths the overall shape of objects, blurs edges, and removes details.

【Gaussian Filters】

	A Gaussian filter attenuates the variations of light intensity in the neighborhood of a pixel. It smooths the overall shape of objects and attenuates details. It is similar to a smoothing filter, but its blurring effect is more subdued.

Nonlinear Filter:

	A nonlinear filter replaces each pixel value with a nonlinear function of its surrounding pixels. Like the linear filters, the nonlinear filters operate on a neighborhood.

【Nonlinear Prewitt Filter】

	The nonlinear Prewitt filter is a highpass filter that extracts the outer contours of objects. It highlights significant variations of the light intensity along the vertical and horizontal axes.

【Nonlinear Sobel Filter】

	The nonlinear Sobel filter is a highpass filter that extracts the outer contours of objects. It highlights significant variations of the light intensity along the vertical and horizontal axes.

【Nonlinear Gradient Filter】

	The nonlinear gradient filter outlines contours where an intensity variation occurs along the vertical axis.

【Roberts Filter】

	The Roberts filter outlines the contours that highlight pixels where an intensity variation occurs along the diagonal axes.

【Differentiation Filter】

	The differentiation filter produces continuous contours by highlighting each pixel where an intensity variation occurs between itself and its three upper-left neighbors.

【Sigma Filter】

	The Sigma filter is a highpass filter. It outlines contours and details by setting pixels to the mean value found in their neighborhood, if their deviation from this value is not significant. The example on the left shows an image before filtering. The example on the right shows the image after filtering.

【Lowpass Filter】

	The lowpass filter reduces details and blurs edges by setting pixels to the mean value found in their neighborhood, if their deviation from this value is large. The example on the left shows an image before filtering. The example on the right shows the image after filtering.

【Median Filter】

	The median filter is a lowpass filter. It assigns to each pixel the median value of its neighborhood, effectively removing isolated pixels and reducing detail. However, the median filter does not blur the contour of objects.

【Nth Order Filter】

	The Nth order filter is an extension of the median filter. It assigns to each pixel the Nth value of its neighborhood when they are sorted in increasing order. The value N specifies the order of the filter, which you can use to moderate the effect of the filter on the overall light intensity of the image. A lower order corresponds to a darker transformed image; a higher order corresponds to a brighter transformed image. 

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