Talk:Scale space implementation

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[edit] Recursive filters figure

The idea with a figure to illustrate the effect of recursive filters is good. To give a better illustration of the discrete filters, however, it would be better to use a rectangular box for each individual value instead of as now a set of points that are connected by straight lines. Then, the graph of each filter would look like a histogram graph with distinct discontinuities between the filter coefficients instead of as now a stepwise linear continuous graph. Tpl 12:15, 2 September 2006 (UTC)

It's very hard to show how two families of sequences compare when using bar graphs. The dots show the discreteness, and the lines help you follow and see what compares with what. I'll play with it and see if I can come up with something better. Dicklyon 15:28, 2 September 2006 (UTC)

[edit] Truncation versus other approaches

tpl, why do you prefer to use a truncated FIR approach to smoothing filters, rather than windowed or a recursive filter? It seems to me that the truncation will always destroy the key property of no introduction of spurious maxima, where the convolution passes the small step edge across a localized signal feature in a non-cascaded application. It's also more more expensive and/or complex to use big FIR convolutions, rather than low-order filters. Dicklyon 23:28, 5 September 2006 (UTC)

If you make use of a sufficiently large filter support regions such that the filter coefficients have started to decrease rapidly (basically exponentially) at the tails, then you can at least in the cases I have encountered circumvent the problem with negative effects on computer vision algorithms due to the truncation error in the scale-space smoothing step. I agree that it will increase the computational work somewhat, but this has turned out to be a highly useful approach for research and algorithm development. Then, once an integrated algorithm has been developed and thoroughly tested, you could start working on improving the computational efficiency by various approximations. In those cases, you may be right that the use of other windowing functions to decrease the support of the filter could be considered. Please, note however that also a windowing filter in the spatial domain violates the semi-group property, while the use of binomial filters or general binomial filters implies a semi-group property with coarser scale steps. The main step to improvement in computational efficiency is however often by transferring algorithms from a uniformly sampled scale-space to a pyramid, or the more flexible notion of hybrid pyramids. Nonwithstanding this, I do in no way want to rule out the use of windowing filters for scale-space implementation. The main reason why I'm hesitant is that I have not seen any papers that investigate this notion with specific regard to integrated scale-space algorithms. Tpl 07:21, 6 September 2006 (UTC)

Thanks, those are good answers. I however prefer to make a few approximations up front to convert to an efficient form of filtering, hence the emphasis on low-order pole-zero filters. By the way, I tried but didn't find a better way to plot the sequence comparisons. I added some more figures and equations to explain things better in terms that typical DSP engineers will get. Dicklyon 07:28, 6 September 2006 (UTC)