词条 | Kernel (image processing) | |||||||||||||||||||
释义 |
In image processing, a kernel, convolution matrix, or mask is a small matrix. It is used for blurring, sharpening, embossing, edge detection, and more. This is accomplished by doing a convolution between a kernel and an image. DetailsThe general expression of a convolution is where is the filtered image, is the original image, is the filter kernel. Every element of the filter kernel is considered by and . Depending on the element values, a kernel can cause a wide range of effects.
The above are just a few examples of effects achievable by convolving kernels and images. OriginThe origin is the position of the kernel which is above (conceptually) the current output pixel. This could be outside of the actual kernel, though usually it corresponds to one of the kernel elements. For a symmetric kernel, the origin is usually the center element. ConvolutionConvolution is the process of adding each element of the image to its local neighbors, weighted by the kernel. This is related to a form of mathematical convolution. It should be noted that the matrix operation being performed - convolution - is not traditional matrix multiplication, despite being similarly denoted by *. For example, if we have two three-by-three matrices, the first a kernel, and the second an image piece, convolution is the process of flipping both the rows and columns of the kernel and then multiplying locally similar entries and summing. The element at coordinates [2, 2] (that is, the central element) of the resulting image would be a weighted combination of all the entries of the image matrix, with weights given by the kernel: The other entries would be similarly weighted, where we position the center of the kernel on each of the boundary points of the image, and compute a weighted sum. The values of a given pixel in the output image are calculated by multiplying each kernel value by the corresponding input image pixel values. This can be described algorithmically with the following pseudo-code: '''for each''' ''image row'' '''in''' ''input image'': '''for each''' ''pixel'' '''in''' ''image row'': '''set''' ''accumulator'' to zero '''for each''' ''kernel row'' '''in''' ''kernel'': '''for each''' ''element'' '''in''' ''kernel row'': '''if''' ''element position'' corresponding* to ''pixel position'' '''then''' '''multiply''' ''element value'' corresponding* to ''pixel value'' '''add''' ''result'' to ''accumulator'' '''endif''' '''set''' ''output image pixel'' to ''accumulator''
If the kernel is symmetric then place the center (origin) of kernel on the current pixel. Then kernel will be overlapped with neighboring pixels too. Now multiply each kernel element with the pixel value it overlapped with and add all the obtained values. Resultant value will be the value for the current pixel that is overlapped with the center of the kernel. If the kernel is not symmetric, it has to be flipped both around its horizontal and vertical axis before calculating the convolution as above.[1] Edge HandlingKernel convolution usually requires values from pixels outside of the image boundaries. There are a variety of methods for handling image edges.
The nearest border pixels are conceptually extended as far as necessary to provide values for the convolution. Corner pixels are extended in 90° wedges. Other edge pixels are extended in lines.
The image is conceptually wrapped (or tiled) and values are taken from the opposite edge or corner.
The image is conceptually mirrored at the edges. For example, attempting to read a pixel 3 units outside an edge reads one 3 units inside the edge instead.
Any pixel in the output image which would require values from beyond the edge is skipped. This method can result in the output image being slightly smaller, with the edges having been cropped.
Any pixel in the kernel that extends past the input image isn't used and the normalizing is adjusted to compensate. NormalizationNormalization is defined as the division of each element in the kernel by the sum of all kernel elements, so that the sum of the elements of a normalized kernel is one. This will ensure the average pixel in the modified image is as bright as the average pixel in the original image. References1. ^http://www.songho.ca/dsp/convolution/convolution2d_example.html
External links
2 : Image processing|Feature detection (computer vision) |
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