Laws' Texture Measures
The texture energy measures developed by Kenneth Ivan Laws at the University of Southern California have been ud for many diver applications. The measures are computed by first applying small convolution kernels to a digital image, and then performing a nonlinear windowing operation. We will first introduce the convolution kernels that we will refer to later.
The 2-D convolution kernels typically ud for texture discrimination are generated from the following t of one-dimensional convolution kernels of length five:
L5 = [ 1 4 6 4 1 ]
E5 = [ -1 -2 0 2 1 ]
S5 = [ -1 0 2 0 -1 ]
W5 = [ -1 2 0 -2 1 ]x77108
去你家玩好吗 R5 = [ 1 -4 6 -4 1 ]
The mnemonics stand for Level, Edge, Spot, Wave, and Ripple. Note that all kernels except L5 are zero-sum. In his disrtation, Laws also prents convolution kernels of length three and ven, and discuss the relationship between different ts of kernels.
From the one-dimensional convolution kernels, we can generate 25 different two-dimensional convolution kernels by convolving a vertical 1-D kernel with a horizontal 1-D kernel. As an example, the L5E5 kernel is found by convolving a vertical L5 kernel with a horizontal E5 kernel. Of the 25 two-dimensional convolution kernels that we can generate from the one-dimensional kernels above, 24 of them are zero-sum; the L5L5 kernel is not. A listing of all 5x5 kernel names is given below:
L5L5 E5L5 S5L5 W5L5 R5L5
L5E5 E5E5 S5E5 W5E5 R5E5
L5S5 E5S5 S5S5 W5S5 R5S5
省钱王 L5W5 E5W5 S5W5 W5W5 R5W5
L5R5 E5R5 S5R5 W5R5 R5R5
The remainder of this document describes how to build up a t of texture energy measures for each pixel in a digital image. This is only a "cookbook" strategy, and therefore most steps are optional.
Step I: Apply Convolution Kernels
Given a sample image with N rows and M columns that we want to perform texture analysis on (i.e. compute texture features at each pixel), we first apply each of our 25 convolution kernels to the image (of cour, for certain applications only a subt of all 25 will be ud.) The result is a t of 25 NxM grayscale images. The will form the basis for our textural analysis.
Step II: Performing Windowing Operation
We now want to replace every pixel in our 25 NxM parate grayscale images with a Texture Energy Measure (TEM) at the pixel. We do this by looking in a local neighborhood (lets u a 15x15 square) around each pixel and summing together the absolute values of the neighborhood pixels. We generate a new t of images, which we will refer to as the TEM images, during this stage of image processing. The following non-linear filter is applied to each of our 25 NxM images.
无忧无虑的意思是
7 7 | |
NEW ( x,y ) = SUM SUM | OLD ( x+i,y+j ) |
i =-7 j =-7 | |
Laws also suggests the u of another filter instead of the "absolute value windowing" filter listed above:
( 7 7 )
NEW ( x,y ) = SQRT ( SUM SUM OLD ( x+i,y+j ) ^ 2 )
( i =-7 j =-7 )
We have at this point generated 25 TEM images from our original image. Lets denote the images by the names of the original convolution kernels with an appended ``T'' to indicate that this is a texture energy measure (i.e. the non-linear filtering has been performed). Our TEM images are named:
L5L5T E5L5T S5L5T W5L5T R5L5T 电影我愿意
L5E5T E5E5T S5E5T W5E5T R5E5T 生地的作用和功效
L5S5T E5S5T S5S5T W5S5T R5S5T
L5W5T E5W5T S5W5T W5W5T R5W5T
书法纸的格式
L5R5T E5R5T S5R5T W5R5T R5R5T
经典文学作品Step III: Normalize Features for Contrast
All convolution kernels ud thus far are zero-mean with the exception of the L5L5 kernel. In accordance with Laws' suggestions, we can therefore u this as a normalization image; normalizing any TEM image pixel-by-pixel with the L5L5T image will normalize that feature for contrast.
After this is done, the L5L5T image is typically discarded and not ud in subquent textural analysis unless a ``contrast'' feature is desirable.
Step IV: Combine Similar Features
For many applications, ``directionality'' of textures might not be important. If this is the ca, then similar features can be combined to remove a bias from the features from dimensionality. For example, L5E5T is nsitive to vertical edges and E5L5T is nsitive to horizontal edges. If we add the TEM images together, we have a single feature nsitive to simple ``edge content''.
