559-2009 | Main / Q0922

Questions from the 09/22 index cards

Can you explain prefiltering? Is it needed if the signal is bandlimited?
How do you do kernel renormalization (*2)
Can you show an example of using filters and let us practice (person was satisfied last time, but I want to give more practice)
more on kernel design
more examples we can work with
could you provide a more complex resampling example?
i understand the theory, but could use more examples
How do the filters we talked about work with the files we're using in our projects?
How does filter width come into play with the targa images? Aren't pixels a certain width anyway?'''

yes, we'll use the pixels as the "unit" by which we measure width.

When do you average a convolution verses summing?

Um, I don't understand the question.

Convolutions

Why is convolution a moving average?

Actually, its a weighted moving average. If you had all the weights be 1/N, then it would be a moving average. (for each point, you average over the neighborhood that "moves" with the point)

What is the most widely used method for dealing with the edges?

I'm not sure what is most common - probably renormalization, since its not a lot of work, cures a bunch of other issues, and gives good results.

For discrete kernels, will the range always be centered at zero?

no, the range can be centered everywhere. for most cases, the center should be zero.

Filters and Kernels

Why is width different than extent?

Extent is the amount of the kernel that is not zero. "width" (as I am using it in class) is the size of the "main bump" of a low pass filter, roughly inversely proportional to the cutoff frequency. Generally, the extent is a multiple of the width, where a larger multiple is used for a higher-quality filter.

Can the "ideal" low pass filter be scaled. What is its cutoff?

Yes. The cutoff frequency is roughly inversely proportional to the width (which for sinc is where it crosses zero)

How is cutoff and width related? How do you pick?
'''Are there cases where the tent filter is the best? or do you always want something better?

All filters have tradeoffs in computation, how well they preserve sharpness, and how

Can a filter ever be too wide? What are the consequences

Yes! if you use too wide a LPF, you'll do more blurring than is necessary, which will lead to a blurrier image than you might like.

Is B-Spline quadratic or cubic?

A B-Spline can actually be any order. Usually, for filtering the cubic is used.

What kernels are used for what tasks? Are there "industry standards?"

Many programs, like photoshop, offer several options. Cubic filters (particularly Mitchell-Netravali) are really common in practice.

Sometimes, you use a sharper (ringing) kernel for upsampling and a blurring kernel (gaussian, bspline) for downsampling.

2D Kernels (seperability, ...)

Should 2D kernels always be symmetric to be seperable?

Being symmetric is a necessary, but insufficient condition for being seperable.

How do you do 2D resampling?
For 2D, we do all the rows first and then all the columns? So the colums depend on the row calculations?

correct

Beyond what we're doing

Would voxel filters be different?

Just as 2D extends 1D, 3D extends it as well - all the squares becomes cubes, etc.

Could the B-Spline filter be used to reduce unwanted signal spikes, like the static on TV

Sortof. Basically, saying that noise is high frequencies is an imperfect approximation. If you just blur everything, then you make everything blurry - not just blurring out the noise. This might be OK. Or not.

Do video cameras work like still cameras (measure the photons using transistors as buckets)?

Yes. Except that they usually don't have a mechanical shutter.

Painting

more on paint-like filters
how do we choose the shape of a brush filter? how to represent it?
how do you make irregular shapes?

Fourier Transforms

Why is the FT of spike chain spike chain, but the FT of constant is box (and vice versa).

The latter is easy to show (DC value). The former is a wierdness of how the integrals work out - see a signal processing book.