Can anyone explain me how can I use the equation of bilateral filter in an image ,each coefficient in equation how can use it on an array and how the filter leave the edge without smoothing ? can anyone help me, please?and why(Ip - Iq) multiply in Iq
The filter computes a weighted sum of the pixel intensities. A normalization factor is always required in a weighted average, so that a constant signal keeps the same value.
The space factor makes sure that the filter value is influenced by nearby pixels only, with a smooth decrease of the weighting. The range factor makes sure that the filter value is influenced by pixels with close gray value only, with a smooth decrease of the weighting.
The idea behind this filter is to average the pixels belonging to the same homogeneous region as the center pixel, as if performing a local segmentation. The average performs smoothing/noise reduction, while restricting to the same region avoids spoling the edges by mixing with pixels of a very different intensity.
Related
First I applied Delaunay Triangulation on an image with 3000 triangles. I measured similarity (SSIM) to original image as 0.75. (The higher value more similar)
Then I applied Delaunay Triangulation on the image's RGB channels separately as 1000 triangles each. Then I combined 3 images and formed the final image. Then I measured similarity of this (SSIM) to original image as 0.65. (The higher value more similar)
In both cases; points chosen randomly, median value of pixels containing triangles choosen as color of the triangle
I did lots of trials but none of the trials showed better results.
Isn't this weird? Think about it. I just use 1000 random triangles on one layer. Then 1000 more on second layer. Then 1000 more on third layer. When these are put on top of it, it should create more than 3000 unique polygons compared to final image triangulation. Because they do not coincide.
a) What can be the reason behind this?
b) What advantages can I obtain when I apply delaunay triangulation on RGB channels separately instead of applying it on image itself? It is obvious I can not get better similarity. But maybe Storage wise can I get better? Maybe in other areas? What can they be?
When the triangles in each layer don't coincide, it creates a low-pass filtering effect in brightness, because the three triangles that contribute to a pixel's brightness are larger than the single triangle you get in the other case.
It's hard to suggest any 'advantages' to either approach, since we don't really know why you are doing this in the first place.
If you want better similarity, though, then you have to pick better points. I would suggest making the probability of selecting a point proportional to the magnitude of the gradient at that point.
I'm trying to code the livewire algorithm but I'm a little stuck because the algorithm explained in the article "Intelligent Scissors for Image Composition" is a little messy and I don't understand complety how to apply certain things for example: How to calculate de local cost map and other stuff.
So please can anyone give a hand and explain it step by step in just simple words?
I would apreciate any help
Thanks.
You should read Mortensen, Eric N., and William A. Barrett. "Interactive segmentation with intelligent scissors." Graphical models and image processing 60.5 (1998): 349-384. which contains more details about the algorithm than the shorter paper "Intelligent Scissors for Image Composition."
Here is a high-level overview:
The Intelligent Scissors algorithm uses a variant of Dijkstra's graph search algorithm to find a minimum cost path from a seed pixel to a destination pixel (the position of the mouse cursor during interactive segmentation).
1) Local costs
Each edge from a pixel p to a pixel q has a local cost, which is a linear combination of the local costs (adjusted by the distance between p and q to account for diagonal pixels):
Laplacian zero-crossing f_Z(q)
Gradient magnitude f_G(q)
Gradient direction f_D(p,q)
Edge pixel value f_P(q)
Inside pixel value f_I(q)
Outside pixel value f_O(q)
Some of these local costs are static and can be computed offline. f_Z and f_G are computed at different scales (meaning with different size kernels) to better represent the edge a pixel q. f_G, f_P, f_I, f_O are dynamically (or have a dynamic component as is the case for f_G) computed for on-the-fly training.
2) On-the-fly training
To prevent snapping to a different edge with a lower cost than the current one being followed, the algorithm uses on-the-fly training to assign a lower cost to neighboring pixels that "look like" past pixels along the current edge.
This is done by building a histogram of image value features along the last 64 or 128 edge pixels. The image value features are computed by scaling and rounding f'_G (where f_G = 1 - f'_G), f_P, f_I, and f_O as to have integer values in [0 255] or [0 1023] which can be used to index the histograms.
The histograms are inverted and scaled to compute dynamic cost maps m_G, m_P, m_I, and m_O. The idea is that a low cost neighbor q should fit in the histogram of the 64 or 128 pixels previously seen.
The paper gives pseudo code showing how to compute these dynamic costs given a list of previously chosen pixels on the path.
3) Graph search
The static and dynamic costs are combined together into a single cost to move from pixel p to one of its 8 neighbors q. Finding the lowest cost path from a seed pixel to a destination pixel is done by essentially using Dijkstra's algorithm with a min-priority queue. The paper gives pseudo code.
The distance transform provides the distance of each pixel from the nearest boundary/contour/background pixel. I don't want closest distance, but I want to get some sort of average measure of the pixel's distance from the boundary/contour in all directions. Any suggestions for computing this distance transform would be appreciated. If there any existing algorithms and/or efficient C++ code available to compute such distance transform, that would be wonderful too.
If you have a binary image of the contours, then you can calculate the number of boundary pixels around each pixel within some windows (using e.g. the integral image, or cv::blur). This would give you something like what you want.
You might be able to combine that with normalizing the distance transform for average distances.
If you want the "average measure of the pixel's distance from the boundary/contour in all directions", then I am afraid that you have to extract the contour and for each pixel inside the pattern, you have to compute the average distance with the pixels belonging to the contour.
An heuristic for a "rough" approximation, would be to compute many distance maps using sources points (they could be the pattern extremities), and for each pixel inside the pattern, then you compute the sum of all distances from the distance maps. But to have the exact measure, you would have to compute as many distance maps as pixels belonging to the contour. But if an approximation is "okay", then this will speed up the processing.
I have 2 2D depth/height maps of equal dimension (256 x 256). Each pixel/cell of the depth map image, contains a float value. There are some pixels that have no information so are set to nan currently. The percentage of non nan cells can vary from ~ 20% to 80%. The depth maps are taken of the same area through point sampling an underlying common surface.
The idea is that the images represent a partial, yet overlapping, sampling of an underlying surface. And I need to align these images to create a combined sampled representation of the surface. If done blindly then the combined images have discontinuities especially in the z dimension (the float value).
What would be a fast method of aligning the 2 images? Translation in the x and y direction should be minimal only a few pixels (~ 0 to 10 pixels). But the float values of one image may need to be adjusted to align the images better. So minimizing the difference between the 2 images is the goal.
Thnx for any advice.
If your images are lacunar, one way is the exhaustive computation of a matching score in the window of overlap, ruling out the voids. FFT convolution will not apply. (Workload = overlap area * X-range * Y-range).
If both images differ in noise only, use the SAD matching score. If they also differ by the reference zero, subtract the average height before comparing.
You can achieve some acceleration by using an image pyramid, but you'll need to handle the voids.
Other approach could be to fill in the gaps by some interpolation method that somehow ensures that the interpolated values are compatible between both images.
Is SIFT a matching approach to replace ZNCC and NCC
or SIFT just provides input to NCC, in other words SIFT is proposed to be used as an alternative to Harris corner detection algorithm?
SIFT is actually a detection, description, and matching pipeline which is proposed by David Lowe. The reason for its popularity is that it works quite well out of the box.
The detection step of SIFT (which points in the image are interesting), comparable to the Harris corner detector that you mentioned, consists of a Difference of Gaussians detector. This detector is a center surround filter and is applied to a scale space pyramid (also applied in things like pyramidal LK tracking) to detect a maximal scale space response.
The description step (what distinguishes this region) then builds histograms of gradients in rectangular bins with several scales centered around the maximal response scale. This is meant as more descriptive and robust to illumination changes etc. than things like raw pixel values, color histograms, etc. There is also a normalization of dominant orientation to get in-plane rotational invariance.
The matching step (for a given descriptor/patch, which out of a pile of descriptors/patches is closest) for SIFT consist of a nearest distance ratio metric which tests for the ratio of distances between the closest match and second closest match. The idea is that if the ratio is low, then the first is much better than the second, thus you should make the match. Else, first and second is about equal and you should reject the match as noise, etc. can easily generate a false match in this scenario. This works better than Euclidean distance in practice. Though for large databases, you'll need vector quantization etc. to keep this working accurately and efficiently.
Overall, I'd argue that the SIFT descriptor/match is a much better/robust approach than NCC/ZNCC though you do pay for it in computational load.