Signal Processing Stack Exchange
Signal Processing Stack Exchange

Questions tagged [scale-space]

30 questions
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Why is the difference of gaussians scale space scale invariant?

I'll use the Scale-invariant feature transform algorithm as an example here. SIFT creates a scale space based on scaled gaussian filtering of an image, and then computes the difference of gaussians to detect potential interest points. These points…
water
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Looking for pratical quantitative comparison metrics for scaled, delayed and warped Signals

[Nota: I have validated the only answer so far, yet more explicit versions are still welcome] The following question is detailed in 1D, with time as the ordinal variable. Similar questions could apply in other dimensions. In several signal…
Laurent Duval
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The Scale Space Theory Understanding

In the scale-space theory the scale-space representation of the signal $f(x), x = (x_1, ..., x_d)$, (in case of image $d = 2$) is given as: $L(x, y; t) = g(x, y; t) * f(x, y)$ where $g(x, y; t)$ is a gaussian kernel with parameter $t$ and $*$ is a…
maximus
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Scalogram (and related nomenclatures) for DWT?

My understanding of the scalogram is that, for a particular row, the scores of the projection of the input signal with the wavelet at a particular displacement is shown. Across rows, the same thing applies, but for dilated version of the wavelet. I…
Spacey
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Losslessness of Laplacian Pyramid

I was just reading up on the Gaussian pyramid and the Laplacian pyramid, used in compression applications of image. The source is here - Carnegie Mellon 16-385 Computer Vision - Spring 2019, Lecture 3 - Image Pyramids and Frequency Domain. The slide…
Sridhar Thiagarajan
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what exactly does scale mean in scale-space theory?

In image processing, scale-space is a technique to represent an image at different scales. But this really confuses me, since I always think that the word scale just means the size of an object, so the scale-space representation of an image shall…
avocado
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SIFT - why s+3 scales per octave?

I have a problem with SIFT that I do not understand. Lowe [1] proposed in his work the s=3 levels of scale are enough for one octave. Afterwards, he mentioned that you need to compute s+3 levels. Why there are 3 and not 2 additional levels required.…
who9vy
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Downsampling and Gaussian Filtering in the Context of Scale Space Pyramids

In the context of scale space image pyramids using Gaussian filters I noticed that it's common to downsample the image after blurring with $\sigma = 2*\sigma_{init}$ . My question is: What is the relation between variance and downsampling? What is…
Matthias Preu
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Function for response over image scales

I want to write code in matlab to find a characteristic scale of an image patch. I have an image patch X, I need to maximize function F(X,sigma) so that sigma is the characteristic sigma. For my experiments, F can be the laplacian of the image,…
matlabit
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Why is it necessary to implement octaves in sift

I've been studying sift very hard for two weeks. I found much materials about scale space. It is very hard to understand scale space depthly. What I've found and confusing things are that 'scale' in scale space means the sigma of gaussian…
jakeoung
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Use Scale Space Representation to Filter Single Image

Currently I hope to use scale space representation to filter one image. Features in one image can be filtered using an Gaussian smooth filter with one optimal sigma. It means different features in one image can be expressed best in different scale…
Jogging Song
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Gaussian Pyramid - How is Subsampling Rate Related to Sigma?

I found a gaussian pyramid implementation in a MOPS paper (feature detection). They use sampling rate $s=2$ and $\sigma=1$ - i.e. to generate a new level of the pyramid, the current level is smoothed with Gaussian blur of that sigma and then…
Libor
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Which sigma to use for edge detection

I know that in many edge detection algorithm the first step is choosing a scale to work on. We actually operate on the chosen scale by applying a gaussian blur on the original image. I wanted to know , what is the relation between the detected…
Elad Walach
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Approximating pixel location in scale space

I'm implementing a scale-space with o octaves and s scale levels in each octave. Each octave is half the size the previous. I have keypoints found in each octave, I need to approximate the real location of the keypoint to their location in the…
matlabit
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Keypoint position and scale in SIFT

If I understood it right, a keypoint is a tuple $$(x,y,\sigma, r),$$ where $x,y$ define the position of the keypoint and $r$ an orientation (given by the most domiant gradiant vector around the keypoint). I'm still not sure about the intention of…
Michals
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