Suppose, the convex hull is a triangle and all the nonextreme points are interior to the triangle then is it possible that quick hull runs in linear time?
Take a look at the wikipedia page. What you are referring to is an output sensitive convex hull algorithm. Small number of hull points result in near linear time algorithms. Same with Akl–Toussaint heuristic.
Related
Are all Gauss points (integration points) also Barlow points (optimal locations to extract stresses during post-processing stage)? I am guessing no. Only for some very specific elements this might be true. If not, do any commercial FEM codes use Barlow points instead of Gauss points to extract stresses?
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 using genetic algorithm in MATLAB to do a two objective optimization problem. I want to know is there any way to plot the population at each generation in a 3d volume? I mean, (f1,f2,n) where f1 is the value of the first objective which i want to minimize and f2 is the value of the second objective that i want to minimize and n is the number of iteration, at the end of each iteration(generation) genetic algorithm produces a pareto-fron which is consists of several points(f1,f2).
how do I plot a volume at the end of optimization to visualize how genetic algorithm converged to a final results? interpolating the convex hulls of each generation maybe?
I think a 3D volume would be very hard to interpret, it would probably be best to do an animation (ideally) in 2D, or if you can't do an animation, plot all iterations on the same plot with e.g. changing color to indicate iterations.
For example:
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.
I found that if I use griddata Method with Cubic Interpolation method, for certain values of x, y, it will return NaN. One post says that this is because the x and y data are very near to convex hull.
Any idea how to fix this?
Edit: Note that I can't make sure that my inputs are monotonously increasing ( thus, gridfit doesn't work). The reason is because I would have to mesh my area ( which could be an irregular polygon in 2D), get all the points before generating the coressponding Z values for each points. My code is as follows:
function ZI=Interpolate3D(scatteredData, boundary)
%scatteredData is the scattered points, boundary is the area that I want to generate 3D surface.
% Given the boundaries, generate mesh first
[element,points]= GenMesh(boundary);
ZI = griddata(scatteredData(:,1),scatteredData(:,2),scatteredData(:,3),points(:,1),points(:,2), 'cubic',{'QJ'});
If your points are outside of the convex hull, you CANNOT get a result other than NaN from griddata using the cubic option. If the point is right on the line, then a NaN may result, depending upon what happens in the least significant bits of the computation.
The issue is that the cubic method uses a triangulation. If your point is outside of the convex hull, then the triangulation fails on that point.
Of course, you CAN use the -v4 method, but there are tremendously good reasons why it has largely been superceded. It uses a distance based interpolation method, where for n data points, a full nxn matrix must be generated. Then a system of equations is solved using that matrix. This will be quite slow for even moderately large problems.
The virtue of the -v4 method is it will extrapolate smoothly without producing nans. This is why it was left in there.
For larger problems where you need a smooth result, and you still wish to extrapolate outside of the convex hull, you can use my gridfit tool. It does do smoothing though, not pure interpolation.
All such methods have tradeoffs that you must resolve for your particular problem.
Since the release of Matlab R2013a you can use scatteredInterpolant instead of griddata.
This has several advantages:
Matlab can perform interpolation as well as extrapolation on a scatteredInterpolant object. You can specify a point outside the convex hull of your scattered data and will still not get a NaN.
Once created, the scatteredInterpolant object can be evaluated multiple times, thus saving computational time compared to calling griddata several times.
On the down side: While you can specify the interpolation and extrapolation methods, cubic is not available but only linear, nearest and natural.
Using scatteredInterpolant your code could look like
F = scatteredInterpolant(scatteredData(:,1),scatteredData(:,2),scatteredData(:,3));
ZI=F(points(:,1),points(:,2));
Are you sure you want cubic interpolation? For some input data the calculated z-nodes could have extreme large values!
I always use -v4 option like the post in your link mentions. You can also play with options used in Qhull via delaunayn, some (but not all) are {'Qt','Qbb','Qc'} http://www.qhull.org/html/qhull.htm