# Questions tagged [scale-space]

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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 ...
3k views

### 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 ...
903 views

### 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 ...
191 views

### Quantitative comparison of scaled-, delayed- and warped-signals

The following question is detailed in 1D, with time as the ordinal variable. Similar questions could apply in other dimensions. In several signal processing techniques, such as blind source ...
3k views

### 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 ...
335 views

### 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 ...
1k views

### 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 ...
4k views

### 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 ...
4k views

### 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 ...
598 views

### 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 ...
2k views

### 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 ...
392 views

### Basic difference between Multi-scale and Multi-resolution images

While working on Convolutional Neural Network (CNN) I saw many research articles working on the Multi-scale images. In the literature of image processing I saw there is also Multi-resolution analysis ...
354 views

### 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 ...
1k views

### 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 ...
1k views

### Computer Vision - Gaussian Pyramid, Scale Space and Pattern Matching

I am planning to implement a pattern matching algorithm using something like correlation as a matching metric. I know that the template I am going to use will, if present, have different sizes in the ...
81 views

### What are the rough steps in obtaining and processing an image from an infrared camera?

I have asked the same question in stackoverflow, but since I am not getting any responses , I am going to ask it again here. My project is to design an interface between an IR camera (Xenics XTM-640) ...
29 views

### Changing Units of Axis

I'm writing a Code for STFT in matlab and I am in the initial stage. Right now I have managed to do the FFT of a small chunk of a time signal. I used zero padding. The problem I am facing is that ...
93 views

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### Analytical expression for salient Blob detection in scale space

I am working on exact mathematical expression which can be obtained in image processing tasks.(I do not know much about image processing but my work is more mathmatical) In Gaussian scale space, we ...
116 views

### Sample keypoint found in multi-scale to one scale (scale space with O octaves)

For a multi-scale keypoints detector, local extremas are found between the scales at EACH octave. The scale-space is implemented as follows: Each octave is downsampled by half from the first image in ...
60 views

### How to calculate x and y of any object inside an image when stretched?

Suppose a image has Height = 200px; Width = 100px; A point in that image which has Y axis = 40px X axis = 30px Now if I ...
1k views

### taylor expansion of scale space function

I see the following expression from http://en.wikipedia.org/wiki/Scale-invariant_feature_transform The quadratic Taylor expansion of the Difference-of-Gaussian scale-space function, with the ...
327 views

### use scale space representation to filter one 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 ...
103 views

### Equal contribution criteria during image pyramid construction

In their paper on Image Pyramids, Burt and Adelson state the following about pyramid generation. An additional constraint is called equal contribution. This stipulates that all nodes at a ...
370 views

### Correct image rotation/scale/moving change

I'm pretty new to Image Processing and am using MatLab. I have an problem were I take an image of light passing trough an set of optical fibers (bundled together) and one were I pass laser energy ...
218 views

### Is there two Types of Scale Space in SURF algorithm?

I couldn't figure out below paragraph on SURF paper and hope that someone can help me to understand it. Bay H., Ess A., Tuytelaars T. Van Gool L. - Speed-Up Robust Features (SURF), page 4, ...