20
votes
Accepted
What Is the Difference between Difference of Gaussian, Laplace of Gaussian, and Mexican Hat Wavelet?
Laplace of Gaussian
The Laplace of Gaussian (LoG) of image $f$ can be written as
$$
\nabla^2 (f * g) = f * \nabla^2 g
$$
with $g$ the Gaussian kernel and $*$ the convolution. That is, the Laplace ...
- 2,770
6
votes
What Is the Difference between Difference of Gaussian, Laplace of Gaussian, and Mexican Hat Wavelet?
The Ricker wavelet, the (isotropic) Marr wavelet, the Mexican hat or the Laplacian of Gaussians belong to be the same concept: continuous admissible wavelets (satisfying certain conditions). ...
- 32.3k
6
votes
What Is the Difference between Difference of Gaussian, Laplace of Gaussian, and Mexican Hat Wavelet?
Let's see how DoG approximates LoG for the 2D case (for an image, e.g.). By derivative theorem of convolution (by associativity and commutativity),
$$\nabla^2[f(x, y) \ast G(x, y)] = \nabla^2 G(x, y) \...
- 163
4
votes
Image Pyramid Without Decimation
For posterity, I'm going to add that you can build the pyramid in this way.
In other words, if you choose the correct standard deviation for the gaussians, you can do all the low-pass filtering to ...
- 41
4
votes
Accepted
2D Multi Scale Dot Enhancement Filter based on Gaussian Filter and Hessian Matrix
Questioner's answer...
sigma have the same units as x and y i.e. number of pixels.
In multi-...
- 215
3
votes
Accepted
Losslessness of Laplacian Pyramid
A very simple example on a $2\times 2$ image
$$I_0=\begin{bmatrix}a&b\\c&d\end{bmatrix}$$
with (very crude Gaussian) low-pass:
$$g=1/4\begin{bmatrix}1&1\\1&1\end{bmatrix}$$
yields a ...
- 32.3k
3
votes
Losslessness of Laplacian Pyramid
Actually the down sampling has no role here.
It is all based on a real simple equation:
$$ I = A + B $$
It is always enough to keep 2 terms of the 3 to restore completely and perfectly the ...
- 20.5k
2
votes
Accepted
Clarification of some known issues in monocular visual odometry
There is only one "ambiguity": world scale is unknown. As you note, given a monocular image sequence observed from a calibrated camera (that is, with known intrinsic parameters), it is ...
1
vote
Accepted
Multiscale Mathematical Morphology Filtering on Python
Thanks to Cris Luengo's remark about saving the values of s, I could get around working the rest out. I stored them in an s_values list which I converted into a ...
- 31
1
vote
What is the difference between single scale and multi scale?
In analogy to Discrete Fourier Transform, you may thing the DFT analyze the data using Multi Frequency approach.
We check the response of the data to different frequencies where the response is based ...
- 20.5k
1
vote
Accepted
At what stage do we compute the approximations and details while performing a DWT?
This expression is more a discretization of a continuous wavelet transform than an actual DWT (discrete wavelet transform), provided $\psi$ is a genuine wavelet. It only computes the wavelet ...
- 32.3k
1
vote
The Concept of scales in Gabor filter
A Gabor filter is a modulated Gaussian. Or said in another way, it is a (complex) wave function windowed by a Gaussian. The wave function determines the frequency and direction, the Gaussian ...
- 2,770
1
vote
Is It Possible to Reconstruct the Original Image from Laplacian Pyramid?
The important message is: "it can indeed be reconstructed", meaning under certain conditions, and not "always".
An image pyramid is hierarchical representation of an image with a collection of ...
- 32.3k
1
vote
Is It Possible to Reconstruct the Original Image from Laplacian Pyramid?
This depends on the order of upsampling and downsampling.
If the order is correct, then you won't throw away anything and thus you should in principle be able to reconstruct the image.
In general:
$$...
- 121
1
vote
Accepted
How Do Steerable Pyramids Work?
We give a precise description of the pyramid algorithm in this paper: http://www.ipol.im/pub/art/2014/79/
It's a wavelet transform.
If you like to use the exact filters you can use Fourier transform ...
1
vote
Accepted
What Is Proper Paper and MATLAB Toolbox Describing and Discussing Wavelet, Ridgelet, Curvelet and Contourlet Transforms in Detail?
On A panorama on multiscale geometric representations, you find a tutorial paper on those directional 2D wavelets, starting with an historical perspective (eg Gaussian & Laplacian pyramids):
and ...
- 32.3k
1
vote
Accepted
Band Limit in Gaussian Pyramid
It's due to the weighting function used in the Gaussian pyramid downsampling.
Lets take a 1D patch(1D patch because it makes our calculation easy and also the kernel is separable) with p10,p11,p12,...
- 700
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