I have come to learn that if I want to overally compare two vectors in my research, the best way is to use Euclidean distance divided by square root of number of arrays. However I don’t know what this equation is called. I will appreciate it if you can share your knowledge with me about that.
Thanks
I found the answer to my question. that term is called "normalized Euclidean distance"
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I am building a program that takes 2 arrays and returns some value showing to what degree they are similar. For example, images with few differences will have a good score, whereas images that are vastly different will have a worse score.
So far the only two algorithms I have come across for this problem are the sum of the squared differences and the normalized correlation.
Both of these will be fairly simple to implement, however I was wondering if there was another algorithm I haven't been able to find that I could use?
Furthermore, which previously mentioned method will be the best? Would be great to know both in terms of their accuracy and efficiency.
Thanks,
Comparing images usually depends on application you are dealing with. Normally distance functions used depends on image descriptor.
Take look at Distance functions
Euclidean Distance
Squared Euclidean Distance
Cosine Distance or Similarity [THIS SHOULD WORK FINE]
Sum of Absolute Differences
Sum of Squared Differences
Correlation Distance
Hellinger Distance
Grid Distance
Manhattan Distance
Chebyshev Distance
statistics distance function
Wasserstein Metric
Mahalanobis Distance
Bray Curtis Distance
Canberra Distance
Binary Distance functions
L0 Norm
Jacard similarity
Hamming Distance
As you are directly comparing images, taking cosine similarity should work for you.
Comparing images well is quite non-trivial.
Just for one example, to get meaningful results you'll need to account for misalignment between the images being compared. If you just compare (for example) the top-left pixel in one image with the top-left pixel in the other, a fairly minor misalignment between the two can make those pixels entirely different, even though a person looking at the images would have difficulty seeing any difference at all.
One way to deal with this would be to start with something similar to the motion compensation used by MPEG 4. That is, break each image into small blocks (e.g., MPEG using 16x16 pixel blocks) and compare blocks in one to blocks in the other. This can eliminate (or at least drastically reduce) the effects of misalignment between the images.
I want an algorithm to be able to find an optimal path between two vertices on a graph (with positive int weights).The thing is my graph is relatively big (up to 100 vertices). I have considered the dijkstra algorithm but as I searched the net most implementions use the adjacency matrix which in my case will be 100x100.
If you could recommend me a certain source to read and learn from , or even better provide me with a c++ implementaion it will be great.
PS: The algorithm needs to output the required route and not just the shortest distance between two points.
Thank you for your time.
Have you looked into A*?
Here's a good article to start reading: http://www.redblobgames.com/pathfinding/a-star/introduction.html
So I have an iterative closest point (ICP) algorithm that has been written and will fit a model to a point cloud. As a quick tutorial for those not in the know ICP is a simple algorithm that fits points to a model ultimately providing a homogeneous transform matrix between the model and points.
Here is a quick picture tutorial.
Step 1. Find the closest point in the model set to your data set:
Step 2: Using a bunch of fun maths (sometimes based on gradiant descent or SVD) pull the clouds closer together and repeat untill a pose is formed:
![Figure 2][2]
Now that bit is simple and working, what i would like help with is:
How do I tell if the pose that I have is a good one?
So currently I have two ideas, but they are kind of hacky:
How many points are in the ICP Algorithm. Ie, if I am fitting to almost no points, I assume that the pose will be bad:
But what if the pose is actually good? It could be, even with few points. I dont want to reject good poses:
So what we see here is that low points can actually make a very good position if they are in the right place.
So the other metric investigated was the ratio of the supplied points to the used points. Here's an example
Now we exlude points that are too far away because they will be outliers, now this means we need a good starting position for the ICP to work, but i am ok with that. Now in the above example the assurance will say NO, this is a bad pose, and it would be right because the ratio of points vs points included is:
2/11 < SOME_THRESHOLD
So thats good, but it will fail in the case shown above where the triangle is upside down. It will say that the upside down triangle is good because all of the points are used by ICP.
You don't need to be an expert on ICP to answer this question, i am looking for good ideas. Using knowledge of the points how can we classify whether it is a good pose solution or not?
Using both of these solutions together in tandem is a good suggestion but its a pretty lame solution if you ask me, very dumb to just threshold it.
What are some good ideas for how to do this?
PS. If you want to add some code, please go for it. I am working in c++.
PPS. Someone help me with tagging this question I am not sure where it should fall.
One possible approach might be comparing poses by their shapes and their orientation.
Shapes comparison can be done with Hausdorff distance up to isometry, that is poses are of the same shape if
d(I(actual_pose), calculated_pose) < d_threshold
where d_threshold should be found from experiments. As isometric modifications of X I would consider rotations by different angles - seems to be sufficient in this case.
Is poses have the same shape, we should compare their orientation. To compare orientation we could use somewhat simplified Freksa model. For each pose we should calculate values
{x_y min, x_y max, x_z min, x_z max, y_z min, y_z max}
and then make sure that each difference between corresponding values for poses does not break another_threshold, derived from experiments as well.
Hopefully this makes some sense, or at least you can draw something useful for your purpose from this.
ICP attempts to minimize the distance between your point-cloud and a model, yes? Wouldn't it make the most sense to evaluate it based on what that distance actually is after execution?
I'm assuming it tries to minimize the sum of squared distances between each point you try to fit and the closest model point. So if you want a metric for quality, why not just normalize that sum, dividing by the number of points it's fitting. Yes, outliers will disrupt it somewhat but they're also going to disrupt your fit somewhat.
It seems like any calculation you can come up with that provides more insight than whatever ICP is minimizing would be more useful incorporated into the algorithm itself, so it can minimize that too. =)
Update
I think I didn't quite understand the algorithm. It seems that it iteratively selects a subset of points, transforms them to minimize error, and then repeats those two steps? In that case your ideal solution selects as many points as possible while keeping error as small as possible.
You said combining the two terms seemed like a weak solution, but it sounds to me like an exact description of what you want, and it captures the two major features of the algorithm (yes?). Evaluating using something like error + B * (selected / total) seems spiritually similar to how regularization is used to address the overfitting problem with gradient descent (and similar) ML algorithms. Selecting a good value for B would take some experimentation.
Looking at your examples, it seems that one of the things that determines whether the match is good or not, is the quality of the points. Could you use/calculate a weighting factor in calculating your metric?
For example, you could weight down points which are co-linear / co-planar, or spatially close, as they probably define the same feature. That would perhaps allow your upside-down triangle to be rejected (as the points are in a line, and that not a great indicator of the overall pose) but the corner-case would be ok, as they roughly define the hull.
Alternatively, maybe the weighting should be on how distributed the points are around the pose, again trying to ensure you have good coverage, rather than matching small indistinct features.
And another algorithm I'm looking for: A free C/C++ implementation of the average distance to nearest neighbour problem.
So basically I have a cloud of points in 3D and I want the average over the distances between all points and their respective nearest neighbours. So easiest way to do this would be to find the nearest neighbour for every point, calculate the distance of that neighbour to the point, and devide the sum of those distances by the number of points. However, there are much better algorithms, as this has much redundancy and approximates run even faster. I'm looking for a free C/C++ implementation of those better algorithms.
An ε-Approximate if fine.
The C++ library FLANN allows you to do "fast approximate nearest-neighbor searches." It's written in C++ and claims to be one of the fastest implementations of this sort of search available.
Hope this helps!
You might try a Quadtree, as described in this question. There are many implementations for your problem in other 3D/2D graphic libraries, too.
I used GEOS, the 'Geometry Engine, Open Source' once in a project some years ago and was very satisfied.
I've got a point in 2d image for example the red Dot in the given picture and a set of n points blue dot (x1,y1)...(xn,yn) and I want to find nearest point to (x0,y0) in a way better than trying all points. Like to have best possible solution. Would appreciate if you share any similar class if you have.
There are many approaches to this, the most common probably being using some form of space partitioning to speed up the search so that it is not O(n). For details, see Nearest neighbor search on Wikipedia.
Most solutions that we could suggest would depend on a little bit more knowledge, I am going to go out on a limb and say that unless you already know that you are short on time. I.e. there are tens of thousands of blue dots or you have to do thousands of these calculations in a short time. "Linear Search" will serve you well enough.
Don't bother calculating the actual distance, save yourself calculating the square root and use this as the "distance".
Most other methods use more complex data structures to sort the points in respect to their geometric arrangement. But are a lot harder to implement.