Talk:Scale space implementation

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)

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)

Refs and such on filtering

I added some refs and details, but was on another machine where I forgot to log in (65.57.245.11). I had received email asking for some clarification of the relations of the van Vliet and Deriche work to the discrete Gaussian. More still needs to be done here, I think. Dicklyon 22:04, 27 July 2007 (UTC)

Scale space representation

I am of the opinion that much of the clarity issues surrounding this article and others could be addressed by creating an article for either scale space representation or scale space framework, and then integrating implementation considerations at particular points within a description of the representation/framework. 70.247.162.84 (talk) 06:45, 21 August 2012 (UTC)

I assume that you have seen that there is an article on scale space, where the description is at a conceptual overview level. If this article on scale-space implementation would be integrated into the overview article, I'm afraid that that could destroy the conceptual overview, by getting down to too technical details. Moreover, for several topics described in the overview article, there are several corresponding issues of implementation that are not at all described in this article on scale-space implementation. If such implementation issues would be added as well for the sake of balance, I'm afraid that that would be much more destructive than helpful, in particular since there are several design issues regarding implementation for which different approaches can be taken. For such issues, the reader is referred to the original references. Tpl (talk) 16:14, 21 August 2012 (UTC)

I have seen the scale space article, and think it is a decent start at a conceptual overview, but it, and some of the related articles are clearly biased toward a practitioner's point of view. I'm not suggesting that practitioner and/or expert knowledge is unwelcome, but I am suggesting that the bias needs to be softened a bit to fit in a neutral encyclopedic format.

By way of comparison, you won't find an article about car repair implementation, even though you will find one about car repair. The encyclopedia format focuses on the "what" and not the "how". What I'm suggesting is that implementation of scale space techniques can be described by describing the "whats" of the implementation: the tools, techniques, people, applications, etc. The "how" is supporting detail for all of these.

More specifically, what I'm saying in this case, is that many of the existing related articles describe a "what" (scale space representation) that doesn't have its own article yet, but would help support the existing articles. Once such an article was written, I think it would become clearer that the implementation is a supporting detail of the representation(s), and the existing text could be redistributed with that perspective.

I am not trying to reduce the content level at all, just trying to make it more useful to readers interested in topical "whats". 70.247.162.84 (talk) 08:43, 25 August 2012 (UTC)

Discrete Gaussian kernel image

The ideal discrete Gaussian kernel (black x, dashed) compared with sampled ordinary Gaussian (red x, solid), for scales $t=[0.5,1,2,4]$

The caption for the Discrete Gaussian kernel describes plots of the discrete and sampled kernels. Basic calculation of the formulas as given in the article itself indicate that the existing labels are incorrect. The solid lines are plots of the sampled kernel and the dashed are plots of the discrete kernel, but the caption says the opposite. I made an edit on 2012-07-17 which corrected the labels, but it was promptly undone. Here are the two highest points in the graph:

The discrete kernel with an example point:

$T(n,t)=e^{-t}I_{n}(t)\,$

$T(0,0.5)=e^{-0.5}I_{0}(0.5)\approx 0.65\,$

The sampled kernel with an example point:

$G(n,t)={\frac {1}{\sqrt {2{\pi }t}}}e^{-n^{2}/2t}$

$G(0,0.5)={\frac {1}{\sqrt {2{\pi }*0.5}}}e^{-0^{2}/(2*0.5)}\approx 0.56$

Even the Wikimedia Commons description (readable by clicking on the image itself) says:

English: Comparison of ideal discrete Gaussians based on Bessel functions (black, dashed) versus sampled Gaussian (red)

I will soon reinstate my edit to match the caption shown in this talk section. --cperk (talk) 05:12, 15 November 2012 (UTC)

Your edit was indistinguishable from vandalism. How could you expect someone to not revert it? Granted, tpl may have been wrong to claim that it introduced errors, based on what you've now shown; I would have just reverted as "indistiguishable from vandalism". Using the edit summary is the quickest way to clarify your intent. Thanks for working on it. I have not checked your work, by the way, in case someone else wonders. Dicklyon (talk) 05:32, 15 November 2012 (UTC)

That was my first edit to any Wikipedia article, so I had something to learn. But I really doubt it is "indistinguishable from vandalism" just because I unknowingly failed to include a summary. In fact, Wikipedia:Vandalism says

"Even if misguided, willfully against consensus, or disruptive, any good-faith effort to improve the encyclopedia is not vandalism. Edit warring over content is not vandalism. Careful consideration may be required to differentiate between edits that are beneficial, detrimental but well-intentioned, and vandalizing. Mislabelling good-faith edits as vandalism can be considered harmful." (Emphasis added.)

It was a simple edit and was apparently not some random, bogus edit. It only took me about 30 seconds to verify those numbers and match them to the graph. tpl could have kindly verified them himself before marking them as errors. I will certainly be more careful about adding summaries, thanks. Perhaps others could be more careful about undoing edits and labeling good-faith edits as vandalism. --cperk (talk) 06:59, 15 November 2012 (UTC)