# Questions tagged [scale-space]

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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 ...
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### 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 ...
24 views

### Creating realization of 2D Gaussian field in Fourier space

I want to generate a 2D Gaussian field with dimensions $L\times L$ with $N^2$ cells each of size $l = L/N$. I'm doing this by producing a realization of this field in Fourier space by producing ...
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 ...
397 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 ...
192 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 ...
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 ...
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) ...
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 ...
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 ...
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 ...
35 views

### 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 ...
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 ...
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 ...
328 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 ...
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### 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 ...