[Insight-users] GradientImageFilter vs. GradientRecursiveGaus sianImageFilter

[Miller, James V (Research)]

Both of these filters are calculating an image where each pixel is a 
CovariantVector whose components are the derivative in x, derivative in y,
etc.

GradientImageFilter performs a simple central difference operation.  I use
this
filter on data that I have already smoothed with another algorithm.  For
instance, the DiscreteGaussianImageFilter, BilateralImageFilter, 
CurvatureFlowImageFilter, or any of the anisotropic diffusion filters.

GradientRecursiveGaussianImageFilter yields a vector field similar to what
you
would get if you convolved an image with several derivate of gaussian
filters. 
Convolving with a derivative of Gaussian is usually better (wrt to numerical
precision) than convolving with a standard Gaussian and then using central 
differences. (Note that DiscreteGaussianImageFilter is a special type of 
Gaussian smoothing that does perform well wrt precision when followed 
by central differences). The GradientRecursiveGaussian does not actually
perform a convolution, but is a constant time algorithm wrt to kernel size. 
Details can be found in the paper referenced in the code.

GradientRecursiveGaussianImageFilter probably uses more memory and
processing
time that GradientImageFilter.  However, this is not an apples to apples 
comparison.  We should compare GradientRecursiveGaussian against
DiscreteGaussian+GradientImageFilter.  Here the memory usage is probably 
a push.  If you are using a large smoothing kernel, then 
GradientRecursiveGaussian will be much faster.

Here are my general rules of thumb:

1. If I am using a large smoothing kernel, I use the
GradientRecursiveGaussian filter.

2. If I am computing several derivatives (first, second, third), I smooth 
the data once, and use central difference type filters.

Jim


-----Original Message-----
From: Michael [mailto:michakuhn at gmx.ch]
Sent: Thursday, August 19, 2004 8:23 AM
To: Insight-users
Subject: [Insight-users] GradientImageFilter vs.
GradientRecursiveGaussianImageFilter


Hi,

what exactly are the differences between the GradientImageFilter and the 
GradientRecursiveGaussianImageFilter (except of the way they calculate 
the gradient image)?

In both cases I would expect an output image that consists of pixels 
with values [derivative1, derivative2, ..., derivativeN]. This means in 
2D pixels with values [derivativeX, derivativeY], where derivativeX 
denotes the derivative in direction x at the pixel position and 
derivativeY the derivative in direction y. Say, we have a pixel at 
position [x0, y0]. Then derivativeX should evaluate to approximately

(GetPixel(x0 + delta, y0) - GetPixel(x0 - delta, y0)) / (2 * delta)

for both filters. Is this correct?

If yes, how do the filters perform (compared to each other) with respect 
to speed and memory consumption?

If no, what are the filters supposed to do?

Thanks,

Michael

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