I am using chessboard to estimate translation vector between it and the camera. Firstly, the intrinsic camera parameters are calculated, then translation vector are estimated using n points detected from the chessboard.
I found a very strange phenomenon: the translation vector is accurate and stable when using more points in the chessboard, and such phenomenon is more obvious when the distance is farer. For instance, the square in the chessboard is 1cm*1cm, when the distance is 3m, translation vector is accurately estimated when using 25 points, while it is inaccurate and unstable using the minimal 4 points. However, when the distance is 0.6m, estimation results of translation vector using 4 points and 25 points are similar, which are all accurate.
How to explain this phenomenon (in theory)? what's the relationship between stable estimation result and distance, and number of points?
Thanks.
When you are using a smaller number of points, the calculation of the translation vector is more sensitive to the noise in coordinates of those points. Point coordinates are noisy due to a finite resolution of the camera (among other things). A that noise only increases with distance. So using a larger number of points should provide for a better estimation.
Related
I want to evaluate the grid quality where all coordinates differ in the real case.
Signal is of a ECG signal where average life-time is 75 years.
My task is to evaluate its age at the moment of measurement, which is an inverse problem.
I think 2D approximation of the 3D case is hard (done here by Abo-Zahhad) with with 3-leads (2 on chest and one at left leg - MIT-BIT arrhythmia database):
where f is a piecewise continuous function in R^2, \epsilon is the error matrix and A is a 2D matrix.
Now, I evaluate the average grid distance in x-axis (time) and average grid distance in y-axis (energy).
I think this can be done by Matlab's Image Analysis toolbox.
However, I am not sure how complete the toolbox's approaches are.
I think a transform approach must be used in the setting of uneven and noncontinuous grids. One approach is exact linear time euclidean distance transforms of grid line sampled shapes by Joakim Lindblad et all.
The method presents a distance transform (DT) which assigns to each image point its smallest distance to a selected subset of image points.
This kind of approach is often a basis of algorithms for many methods in image analysis.
I tested unsuccessfully the case with bwdist (Distance transform of binary image) with chessboard (returns empty square matrix), cityblock, euclidean and quasi-euclidean where the last three options return full matrix.
Another pseudocode
% https://stackoverflow.com/a/29956008/54964
%// retrieve picture
imgRGB = imread('dummy.png');
%// detect lines
imgHSV = rgb2hsv(imgRGB);
BW = (imgHSV(:,:,3) < 1);
BW = imclose(imclose(BW, strel('line',40,0)), strel('line',10,90));
%// clear those masked pixels by setting them to background white color
imgRGB2 = imgRGB;
imgRGB2(repmat(BW,[1 1 3])) = 255;
%// show extracted signal
imshow(imgRGB2)
where I think the approach will not work here because the grids are not necessarily continuous and not necessary ideal.
pdist based on the Lumbreras' answer
In the real examples, all coordinates differ such that pdist hamming and jaccard are always 1 with real data.
The options euclidean, cytoblock, minkowski, chebychev, mahalanobis, cosine, correlation, and spearman offer some descriptions of the data.
However, these options make me now little sense in such full matrices.
I want to estimate how long the signal can live.
Sources
J. Müller, and S. Siltanen. Linear and nonlinear inverse problems with practical applications.
EIT with the D-bar method: discontinuous heart-and-lungs phantom. http://wiki.helsinki.fi/display/mathstatHenkilokunta/EIT+with+the+D-bar+method%3A+discontinuous+heart-and-lungs+phantom Visited 29-Feb 2016.
There is a function in Matlab defined as pdist which computes the pairwisedistance between all row elements in a matrix and enables you to choose the type of distance you want to use (Euclidean, cityblock, correlation). Are you after something like this? Not sure I understood your question!
cheers!
Simply, do not do it in the post-processing. Those artifacts of the body can be about about raster images, about the viewer and/or ... Do quality assurance in the signal generation/processing step.
It is much easier to evaluate the original signal than its views.
I am looking for a clustering algorithm such a s DBSCAN do deal with 3d data, in which is possible to set different epsilons depending on the axis. So for instance an epsilon of 10m on the x-y plan, and an epsilon 0.2m on the z axis.
Essentially, I am looking for large but flat clusters.
Note: I am an archaeologist, the algorithm will be used to look for potential correlations between objects scattered in large surfaces, but in narrow vertical layers
Solution 1:
Scale your data set to match your desired epsilon.
In your case, scale z by 50.
Solution 2:
Use a weighted distance function.
E.g. WeightedEuclideanDistanceFunction in ELKI, and choose your weights accordingly, e.g. -distance.weights 1,1,50 will put 50x as much weight on the third axis.
This may be the most convenient option, since you are already using ELKI.
Just define a custom distance metric when computing the DBSCAN core points. The standard DBSCAN uses the Euclidean distance to compute points within an epsilon. So all dimensions are treated the same.
However, you could use the Mahalanobis distance to weigh each dimension differently. You can use a diagonal covariance matrix for flat clusters. You can use a full symmetric covariance matrix for flat tilted clusters, etc.
In your case, you would use a covariance matrix like:
100 0 0 0 100 0 0 0 0.04
In the pseudo code provided at the Wikipedia entry for DBSCAN just use one of the distance metrics suggested above in the regionQuery function.
Update
Note: scaling the data is equivalent to using an appropriate metric.
I need to optimize the location of 10 Transmitters and 10 Receivers (modeled as points on an aperture plane) so as to minimize a certain objective scalar using Genetic Algorithm toolbox in MATLAB. My question is: I have (10+10)*2 = 40 variables (optimizing x and y positions of each point). How do I model the constraints in the form Ax <= b, such that each point is separated by a minimum distance in both x and y directions from all other points?
I'd model the objective function as the euclidian distance between the points, which you are trying to minimize. Also the transmitters and receivers must have a minimum distance between them. So this distance should be minimum, but greater than the minimum distance of the equipment. I'd look into the dimensions of the plane to identify all the constraints.
I'm calculating displacement from the motion of an accelerometer and using a Kalman filter to improve the displacement accuracy. Please note that I am aware of ineffectiveness of using acceleration to obtain displacement in real scenarios, but in my case displacement is pretty small (like 10 cm over 2–3 seconds).
I am following this paper (PDF). In the paper there are two matrices, Q and R, for noise modeling and they are set such that displacement error is minimized. The authors tested the above with synthetic acceleration data of a known covariance to use the same in matrices Q and R.
I decided to vary the particular covariance and find its corresponding minimum error in displacement. But in my case there is no change in displacement at any value of covariance. Any help?
What is the best method for finding impulse peaks (dirac delta) in a 2d matrix.
More specifically, I would like to find the harmonic frequencies of a given image and so I need to find impulse peaks in the image absolute value DFT.
I thought of using findpeaks but there's no 2d version. I also saw earlier posts regarding finding ordinary peaks using imdilate and/or imextendedmax but those find all the peaks in a 2d matrix whereas I am only interested in impulse peaks. I am sure DSP people have a common recipe for this...
Please Help,
Thanks
What you want to do is find peaks with high contrast. Thus, you need a way to identify local maxima, plus a way to measure the difference between the peak and the surrounding values. Thresholding on this difference will identify the impulse peaks for you.
Assuming your input signal is called signal
%# dilate to find, for every pixel, the maximum of its neighbors
dilationMask = ones(3);
dilationMask(5) = 0;
dilSignal = imdilate(signal, dilationMask);
%# find all peaks
%# peaks = signal > dilSignal;
%# find large peaks peaks by thresholding, i.e. you accept a peak only
%# if it's more than 'threshold' higher than its neighbors
peaks = (signal - dilSignal) > threshold;
peaks is a logical array with 1's wherever there is a good peak. You can use it to read peak heights from signal with signal(peaks), and to find coordinates using find(peaks).
This paper I wrote contains Matlab source code for fast local peak detection in 2D. It works similar to imregionalmax() in Mathworks Image Processing Toolbox but allows you to specify a local neighborhood radius: bigger radius -> sparser peaks.
Since you expect sparse impulses, the nonmaxsupp_scanline() function may be suitable for you.
The findpeaks algorithm is pretty trivial; if an element is bigger than both its neighbours, then it is a peak. Writing a 2D version of this should be pretty simple.