How can i represent a 3D coordinate as a singular value?
I need this since the libsvm requieres the input data to be 1-dimensional?
Thank you
You can simply use 3 features for each coordinate. (They even write so in their README)
Related
The following image is the example that was given in my computer vision class. Now I cant understand why we are getting 2 unique values of f. I can understand if mxf and myf are different, but shouldn't the focal length 'f' be the same?
I believe you have an Fx and a Fy. This is so that the the matrix transforms on f can scale f in two directions x and y. IIRC this is why you get 2 f numbers
If really single f wanted, it should be modeled in the camera model used in calibration.
e.g. give the mx,my as constants to the camera model, and estimate the f.
However, perhaps the calibration process that obtained that K was not that way, but treated the two elements (K(0,0) and K(1,1)) independently.
In other words, mx and my were also estimated in the sense of dealing with the aspect ratio.
The estimation result is not the same as the values of mx and my calculated from the sensor specifications.
This is why you got 2 values.
I‘m quite bad at programming, so please bear with me. I‘m not even sure what the concept I need right now is called, so i don’t know what to google for or write in the title of this post.
My issue is, I numerically integrated a function on Mathematica and have a function F that depends on 2 inputs X and Y. Those inputs form a 2x2 grid. To visualize my solution, I would need a 3D graph.
Now I want to compare this to my analytical solution (/approximation) A, which I know only depends on one input Z, which is the ratio of X/Y. To visualize it, I only need a 2d Graph.
My issue now is, that I‘m not sure how to effectively filter that part of my numerical solution F so that I only consider the outputs with various ratios X/Y. This way, I could easily compare it to my analytical solution by only using a 2d graph.
I hope some of you understand my gibberish. I apologize for not being able to properly explain what I need in the correct language. I would be glad if some of you might be able to help me. Any help is appreciated.
Is my understanding correct? You have a numerically integrated function, F which maps a pair of numbers to a scalar:
F: (x,y) -> (z)
Then, there's another function, A, which takes a scalar and maps it to another scalar:
A: (b) -> (c)
and b is itself the ratio of x and y from before:
b = x/y
And you'd like to compare the outputs of F and A, i.e. compare z to c, as I've defined them here?
One thing you can do is sample the inputs to F that you already have, and then query A with the ratio of those inputs, and compare the output.
To put it another way, you can say, "for this x and this y, I know the output of F is this. Then, when I divide them and put them into A I get this."
Then, you could make a heatmap, say, where one of the axes is the x-value and the other axis is the y-value, and the color corresponds to F(x, y) - A(x/y)
Say you have the matrix given by three arrays, being:
x = N-dimensional array.
y = M-dimensional array.
And z is a set of "somewhat random" values from -0.3 to 0.3 in a NxM shape. I need to create a plot in which the x values are in the x-axis, y values are in the y-axis and using z as the source to indicate the intensity of each pixel with a color map.
So far, I have tried using
plt.contourf(x,y,z)
and the resulting plot is very nice for me (attached at the end of this paragraph), but a smoothing is automatically applied to the plot! I need to be able to distinguish the pixels and I cannot find a way to do it.
contourf result
I have also studied the possibility of using
ax.matshow(z)
in order to sucesfully see the pixels... but then I am struggling trying to personalize the x and y axis, since only the index of the pixel is shown (see below).
matshow result
Would you please give me some ideas? Thank you.
Without more information on your x,y data it's hard to know, but I would guess you are looking for pcolormesh.
plt.pcolormesh(x,y,z)
This would take the x and y data as input and hence shows the z data at the appropriate coordinates.
You can use imshow with the keyword interpolation='nearest'.
plt.imshow(z, interpolation='nearest')
Let's say I know two persons are standing at GPS location A and B. A is looking at B.
I would like to know B's (x, y, z) coordinates based on A, where the +y axis is the direction to B (since A is looking at B), +z is the vertically to the sky. (therefore +x is right-hand side of A)
I know how to convert a GPS coordinate to UTM, but in this case, a coordinate system rotation and translation seem needed. I am going to come up with a calculation, but before that, will there be some codes to look at?
I think this must be handled by many applications, but I could not find so far.
Convert booth points to 3D Cartesian
GPS suggest WGS84 so see How to convert a spherical velocity coordinates into cartesian
Construct transform matrix with your desired axises
see Understanding 4x4 homogenous transform matrices. So you need 3 perpendicular unit vectors. The Y is view direction so
Y = normalize(B-A);
one of the axises will be most likely up vector so you can use approximation
Z = normalize(A);
and as origin you can use point A directly. Now just exploit cross product to create X perpendicular to both and make also Y perpendicular to X and Z (so up stays up). For more info see Representing Points on a Circular Radar Math approach
Transfrom B to B' by that matrix
Again in the QA linked in #1 is how to do it. It is simple matrix/vector multiplication.
Basically, I have a set of up to 100 co-ordinates, along with the desired tangents to the curve at the first and last point.
I have looked into various methods of curve-fitting, by which I mean an algorithm with takes the inputted data points and tangents, and outputs the equation of the cure, such as the gaussian method and interpolation, but I really struggled understanding them.
I am not asking for code (If you choose to give it, thats acceptable though :) ), I am simply looking for help into this algorithm. It will eventually be converted to Objective-C for an iPhone app, if that changes anything..
EDIT:
I know the order of all of the points. They are not too close together, so passing through all points is necessary - aka interpolation (unless anyone can suggest something else). And as far as I know, an algebraic curve is what I'm looking for. This is all being done on a 2D plane by the way
I'd recommend to consider cubic splines. There is some explanation and code to calculate them in plain C in Numerical Recipes book (chapter 3.3)
Most interpolation methods originally work with functions: given a set of x and y values, they compute a function which computes a y value for every x value, meeting the specified constraints. As a function can only ever compute a single y value for every x value, such an curve cannot loop back on itself.
To turn this into a real 2D setup, you want two functions which compute x resp. y values based on some parameter that is conventionally called t. So the first step is computing t values for your input data. You can usually get a good approximation by summing over euclidean distances: think about a polyline connecting all your points with straight segments. Then the parameter would be the distance along this line for every input pair.
So now you have two interpolation problem: one to compute x from t and the other y from t. You can formulate this as a spline interpolation, e.g. using cubic splines. That gives you a large system of linear equations which you can solve iteratively up to the desired precision.
The result of a spline interpolation will be a piecewise description of a suitable curve. If you wanted a single equation, then a lagrange interpolation would fit that bill, but the result might have odd twists and turns for many sets of input data.