gradient input output gradient
input
List of images for which gradient images are to be calculated.
output
List of output images. The number of output images must equal the number of
input images. If the input image name equals the output image name the
convolved image will replace the input image.
gradient
The gradient filters are a set of 8 three by three kernels identified by the
angle of maximum response as measured counter-clockwise to the x axis. The
kernels approximate the gradient operator, which is defined as the slope of
the intensity distribution in an image. The eight supported gradient
operators are listed below.
0 , 180
Calculate the gradient image along a 0 or 180 degree angle.
These options approximate the d/dx operator.
Option "0" produces a maximum response for pixel values which
increase with increasing x, whereas option "180" produces a maximum
response for pixel values which decrease with increasing x.
90 , 270
Calculate the gradient image along a 90 or 270 degree angle.
These options approximate the d/dy operator.
Option "90" produces a maximum response for pixel values which
increase with increasing y, whereas option "270" produces a maximum
response for pixel values which decrease with increasing y.
45 , 225
Calculate the gradient image along a 45 or 225 degree angle.
Option "45" produces a maximum response for pixel values which increase
along a line at 45 degrees counter-clockwise to the x axis.
Option "225" produces
a maximum response for pixel values which increase along a line at 225
degrees to the x axis.
135 , 315
Calculate the gradient image along a 135 or 315 degree angle.
Option "135" produces a maximum response for pixel values which increase
along a line at 135 degrees counter-clockwise to the x axis.
Option "315" produces
a maximum response for pixel values which increase along a line at 315
degrees to the x axis.
boundary = nearest
The algorithm used to compute the values of out of bounds pixels. The
options are:
nearest
Use the value of the nearest boundary pixel.
constant
Use a constant value.
reflect
Generate a value by reflecting around the boundary.
wrap
Generate a value by wrapping around to the opposite side of the image.
constant = 0.
The constant for constant-valued boundary extension.
GRADIENT convolves the list of images specified by input with one of eight three by three gradient kernels specified by gradient and places the output images in output. If the image names in output equal the image names in input the gradient operation is performed in place and the original images are overwritten. Out of bounds pixels are computed using the algorithm specified by boundary.
GRADIENT acts like a simple edge detector or high pass filter which is sensitive to both the magnitude and direction of changes in intensity in an image. For example, if an image's pixel values are specified by the sum of their x and y coordinates (z = x + y) and boundary extension effects are ignored, the "0", "45", "90", "135", "180", "225", "270", and "315" gradient kernels will each produce a constant image containing the numbers 1, sqrt (2), 1, 0, -1, -sqrt (2), -1, and 0 respectively.
The eight gradient filters are listed below. The I[*,*] are the elements of the input image and the O[*,*] are elements of the output image.
0
- I[-1,1] + 0*I[0,1] + I[1,1]
O[0,0] = - I[-1,0]*sqrt(2) + 0*I[0,0] + I[1,0] * sqrt(2)
- I[-1,-1] + 0*I[0,-1] + I[-1,-1]
45
+ I[-1,1]*0 + I[0,1] + I[1,1]/2/sqrt(2)
O[0,0] = - I[-1,0] + I[0,0]*0 + I[1,0]
- I[-1,-1]/2/sqrt(2) - I[0,-1] + I[1,-1]*0
90
+ I[-1,1] + I[0,1]*sqrt(2) + I[1,1]
O[0,0] = + I[-1,0]*0 + I[0,0]*0 + I[1,0]
- I[-1,-1] - I[0,-1]*sqrt(2) - I[-1,-1]
135
+ I[-1,1]/2/sqrt(2) + I[0,1] + I[1,1]*0
O[0,0] = + I[-1,0] + I[0,0]*0 - I[1,0]
+ I[-1,-1]*0 - I[0,-1] - I[1,-1]/2/sqrt(2)
180
+ I[-1,1] + 0*I[0,1] - I[1,1]
O[0,0] = + I[-1,0]*sqrt(2) + 0*I[0,0] - I[1,0]*sqrt(2)
+ I[-1,-1] + 0*I[0,-1] - I[-1,-1]
225
+ I[-1,1]*0 - I[0,1] - I[1,1]/2/sqrt(2)
O[0,0] = + I[-1,0] + I[0,0]*0 - I[1,0]
+ I[-1,-1]/2/sqrt(2) + I[0,-1] + I[1,-1]*0
270
- I[-1,1] - I[0,1]*sqrt(2) - I[1,1]
O[0,0] = + I[-1,0]*0 + I[0,0]*0 + I[1,0]*0
+ I[-1,-1] + I[0,-1]*sqrt(2) + I[-1,-1]
315
- I[-1,1]/2/sqrt(2) - I[0,1] + I[1,1]*0
O[0,0] = - I[-1,0] + I[0,0]*0 + I[1,0]
+ I[-1,-1]*0 + I[0,-1] + I[1,-1]/2/sqrt(2)
1. Calculate the gradient in the 180 degree direction using nearest neighbour boundary extension.
cl> gradient m83 m83.odeg 180
GRADIENT requires approximately 2.0 cpu seconds to convolve a 512 square real image with a 3 by 3 gradient kernel on a Sparc Station 1.
convolve, gauss, laplace, boxcar,