kd-tree | An implementation of k-d tree | Dataset library
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An implementation of k-d tree
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QUESTION
Im doing an art project where i really need to be able to divide a rectangle in a random way. Ive have been searching alot for this but have not found anything i really can implement in proccesing. The idea is after, reading this thread Break up a square or rectangle into a large number of randomly sized squares or rectangles to use a KD-tree or an divide conquer algorithm. I only just learned how a basic Binary Tree works so im a bit lost how to implement this in proccesing code.
...ANSWER
Answered 2022-Apr-07 at 14:02This (p5js) sketch divides a rectangular plane in random sized smaller rectangles and seems suitable for your need.
The sketch slices (either horizontally or vertically) the plane recursively until a "slice limit" is reached for each recursive call, upon which a rectangle is returned.
I ported the sketch from js to Java Processing here. In fact, it can be easily called from the parent project (PGS) with:
PShape division = PGS_Tiling.rectSubdivsion(double width, double height, int maxDepth);
QUESTION
I know this is a super basic question, but I'm stuck.
I am attempting to create a data frame. I want to create a data frame that contains the results of the for loop.
...ANSWER
Answered 2021-Nov-03 at 03:00In the inner for loop, you are appending the same num_list
for the entire for loop length. I think changing that part should do it. And for the pd.DataFrame
, the data should not be a list, it should be in dictionary format.
QUESTION
I am creating a small euclidean clustering node for the point cloud, utilizing PCL's implementation of the KD tree.
Currently, my subscriber definition looks like this,
...ANSWER
Answered 2021-Oct-14 at 19:10You can replace
QUESTION
Currently, I'm working on image stitching of aerial footage. I'm using the dataset, get from OrchardDataset. First of all, thanks to some great answers on stackoverflow, especially the answer from @alkasm (Here and Here). But I having an issue, as you can see below at Gap within the stitched image
section.
I used the H21
, H31
, H41
, etc to wrap the images. The stitched image using H21
is excellent, but when wrap the img3
to current stitched image
using H31
, result shown terrible alignment between img3
and current stitched image
. As the more images I wrap, the gap gets bigger and the images totally not well aligned.
Does the brillant stackoverflow community have an ideas on how can I solve this problem?
These are the steps I use to stitch the images:
- Extract the frame every second from the footage and undistort the image to get rid of fish-eye effect using the provided camera calibration matrix.
- Compute the SIFT feature descriptors. Set up macther using FLANN kd-tree and find matches between the images. Find the Homography (
H21
,H32
,H43
and etc, whereH21
refer to the homography which warpsimag2
into coordinates ofimg1
) - Compose the homography with the previous homographies to get net homography using the method suggested in Here. (Compute
H31
,H41
,H51
, etc) - Wrap the images using the answer provided in Here.
Gap within the stitched image:
I'm using the first 10 images get from OrchardDataSet.
Here's portion of my script:
main.py
ref_img
is the first frame (img1
). AdjHomoSet
contain the images to be wraped (img2
, img3
, img4
, etc). AccHomoSet
contain the net homography (H31
, H41
, H51
, etc)
ANSWER
Answered 2021-Mar-09 at 09:54Eventually I changed the way of warping the image using the approach provided by Jahaniam Real Time Video Mosaic. He locates the reference image at the middle of preset size of blank image and compute the subsequent homography and warp the adjacent images to the reference image.
QUESTION
I have a Set of n points and a more or less arbitrary circle. Now I want to check if the circle contains at most k of the points.
Right now I'm just brute force testing all of the points. Since I need to answer this question for a lot of circles, a preprocessing time of up to n²log(n) would be fine.
The optimal data structure would most likely be the order k-Voronoi Diagram (not the one for dimension k), but I would need to implement it myself and therefore I would like to know if I have other (simpler) options.
Another Idea for some speed up would be using a KD-Tree.
I would like to know, if I'm missing another way to do it.
...ANSWER
Answered 2021-Feb-18 at 08:40It seems that you are after a fixed-radius near-neighbor count query.
Using a KD-tree (K=2), you can list the points in a given circle, in time roughly O(k + Log n). This is achieved by overlapping the circle with the rectangles of the KD-tree subdivision. When a rectangle is wholly contained in the circle, there is no need to subdivide further, all points inside the rectangle are inside the circle.
So you can enhance the tree with the number of points contained in every node of the tree. This will lower the running time to O(m + Log n) where m is the number of rectangles contained in or split by the circle. It is also possible to stop subdividing when a rectangle contains less than a predefined number of points, and test them by brute force.
These are heuristics. You have to test them on your cases to see if they are worth.
Update:
Just an idea, not really investigated: Vantage-point trees are appropriate for k-nearest-neighbors searches and they partition the plane using circles. That might better blend with circle queries.
https://en.wikipedia.org/wiki/Vantage-point_tree#Searching_through_a_vantage-point_tree
QUESTION
I am trying to create a kd-tree through scipy's KD_tree class built by objects rather than pure coordinates. The objects has a (x,y) tuple, and the tree is based upon this, but i would like to include the object itself as the node/in the node.
Is there some "easy" approach to this? Had a look on scipy kdtree with meta data, which says to use a third dimension as a object pointer(?). Wouldn't the tree then apply this value to the comparison of neighbors? I am also in the same boat as this gentleman, where creating my own kd-tree would be nice to skip for now.
PS. This is my first post, so be gentle with me ;)
...ANSWER
Answered 2021-Feb-09 at 12:53The API of scipy's KdTree wants a 2D array of coordinates as input and not any sort of object array. In this array the rows are the points and the cols the coordinates of those points.
In the question you link to, he doesn't mean that there is a third dimension but a third index. Suppose you are looking for a single nearest neighbor and you query using some point, the function will return a distance and an index. The index is a reference into the array with which you built the tree. The distance is the difference in distance between your query point and the tree point.
So to use this tree you could keep two arrays. One with the object coordinates and a second one with the objects. They should be in the same order, so that when a query returns an index, they mean the same thing in both arrays.
PS. This is my first answer, so also be gentle :D
QUESTION
I know I can use a data structure such as the kd-tree to look for the k nearest points to each point in the plane (using the Euclidean distance). But I've already constructed a Delaunay triagulation in my program, so I'd like to find the k nearest neighbors more efficiently by taking adavntage of the Delaunay triangulation. I'm using Matlab, and the delaunayTriangulation class allows to query only the first nearest neighbor to a given point. How can I find the k nearest neighbors in MATLAB using the Delaunay triangulation? Or otherwise, if I have to implement myself the k nearest neighbors search algorithm from the Delaunay triangulation, can you point me out to such an algorithm?
...ANSWER
Answered 2020-Dec-02 at 16:46If you are only interested in finding k points nearest to a centroid, then forget you have triangles. You have a cloud of points (that cloud be related to triangles, but its irrelevant) that you need to find kn nearest neighbors to it.
knnsearch()
is sufficient.
Original answer:
When I had this problem, I found 2 efficient solutions.
if you want K nearest neighbours to an arbitrary point, you need to build a tree. I used R*-trees because they allow volumetric objects, but if you only consider the centroid of the elements then you can survive with an easier to code tree.
If you want K nearest neighbors to an element itself, the best way I found is by building a network graph. A Delaunay triangulation is not structure and finding in this list gets intractable soon as you increase it, so you need to enforce some order. You need to build a graph that will order these elements and store their neighbours, so you can simply query neigbours in distance from the element if your interest.
I found no MATLAB function to solve this for me and I ended up writing my own stuff. This was in a larger framework of using tetrahedra as image basis for computed tomography, so there is a lot of extra stuff in that repo and things may need touching here and there. Use at your own risk.
QUESTION
Given a square grid with side N. Also given a set of input points on the grid. Need to find another set of points on the grid (can be multiple) that have the maximal Manhattan distance from the given input points.
For example with N = 4
and input [p1:{0, 0}, p2:{3, 3}]
the output should be [{0, 3}, {1, 2}, {2, 1}, {3, 0}]
with the distance equal to 3.
ANSWER
Answered 2020-Oct-01 at 12:06You should use a breadth-first search, starting with all the given points, to simultaneously find the distance of every cell from its nearest point. This takes linear time and is pretty easy to code.
Then find the highest distance (or just remember it, since it will be the last one you wrote), and return all the cells with that distance.
That will work pretty well if your points aren't too sparse. If they're separated by vast distances, then you'll need an algorithm the grows with the number of points instead of the size of the grid. That would be based on calculating the Manhattan-distance Voronoi diagram, since all the points you want to return are on it.
QUESTION
In these slides (13) the deletion of a point in a kd-tree is described: It states that the left subtree can be swapped to be the right subtree, if the deleted node has only a left subtree. Then the minimum can be found and recursively be deleted (just as with a right subtree).
This is because kd-trees with equal keys for the current dimensions should be on the right.
My question: Why does the equal key point have to be the right children of the parent point? Also, what happens if my kd-tree algorithm returns a tree with an equal key point on the left?
For example: Assume the dataset (7,2), (7,4), (9,6) The resulting kd-tree would be (sorted with respect to one axis):
...ANSWER
Answered 2020-Aug-23 at 23:28There is no hard and fast rule to have equal keys on right only. You can update that to left as well.
But doing this, you would also need update your algorithms of search and delete operations.
Have a look at these links:
https://www.geeksforgeeks.org/k-dimensional-tree/
https://www.geeksforgeeks.org/k-dimensional-tree-set-3-delete/
QUESTION
I am trying to use Kdtree data structure to remove closest points from an array preferablly without for loops.
...ANSWER
Answered 2020-Jun-02 at 02:45Your points
array is a Nx2 matrix. Your ind
indices are a list of row indices. What you need is to specify the axis along which you need deletion, ultimately this:
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