Digital Gradient
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Next: Compass Gradient Operations Up: gradient Previous: The Gradient Operator
Digital Gradient
For discrete digital images, the derivative in gradient operation
![\begin{displaymath}D_x[f(x)]=\frac{d}{dx}f(x)=\lim_{\Delta x \rightarrow 0}\frac{f(x+\Delta x)-f(x)}{\Delta x} \end{displaymath}](http://images0.cnblogs.com/blog/626816/201405/041201452831068.png)
becomes the difference
![\begin{displaymath}D_n[f[n]]=f[n+1]-f[n],\;\;\;\;\mbox{or}\;\;\;\;\frac{f[n+1]-f[n-1]}{2} \end{displaymath}](http://images0.cnblogs.com/blog/626816/201405/041201455955396.png)
Two steps for finding discrete gradient of a digital image:
- Find the difference: in the two directions:
- Find the magnitude and direction of the gradient vector:
The differences in two directions and
can be obtained by convolution with the following kernels:
- Roberts
or - Sobel (3x3)
- Prewitt (3x3)
- Prewitt (4x4)
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Next: Compass Gradient Operations Up: gradient Previous: The Gradient OperatorRuye Wang 2013-11-08