Overlaying and Comparing Two Sets of Co-Ordinates

Hello all

I have been using Matlab as a fancy calculator for some time now but always wanted to do more with it.

So part of trying to learn Matlab I was wanted to tackle an actual problem which I was hoping the community could help with.

I have 2 x sets of data, they are data set 1 and data set 2.

Data set 1contains a list of X Y co-ordinates (which I have created a matrix for), the data relates to an outline of a building.

Data set 2 also contains a list of X Y co-ordinates (which I have also created a matrix for), this data relates to the outline of the same building, the only difference is that data set 2 contains more data X Y co-ordinates and the values of each X and Y differ slightly.

Plotting these data sets gives me the following:-

What I am trying to do is overlay data set 2 with data set 1 such that the best fit is found.

Once the images are overlaid as best as they can I then want to compare the original X Y co-ordinates of data set 2 with the adjusted/best fit co-ordinates of data set 2 to see the difference.

I am struggling with how to overlay the two sets of co-ordinates to produce a best fit – any ideas?

Thank you.

[Matt J]

What kind of transformations of data set 2 (to match data set 1) are you willing to allow? Translations? Rotations? Something even more complicated?

[John hope]

Hi Matt

The allowable transformations include:-

1) +ve & -ve translations

2) Reflection

3) Rotation

4) Mirroring

Any type of Scaling i.e Dilation/Compression/Contraction is not allowed

thoughts?

Thanks

Answer 1

[Matt J]

I haven't used it myself, but this implementation of Iterative Closest Point seems pretty popular

https://www.mathworks.com/matlabcentral/fileexchange/12627-iterative-closest-point-method

[John hope]

Hi Matt

thank you for pointing me in the right direction.

I have downloaded the the ICP code and have adapted to fit my needs and it appears to work well.

I know that you said that you have not used this before but i have to ask as it is bugging me.

There is a section of code which i have no idea what it is used for, it is:-

% % Transform data points to their start positions
v1=0.6*(2*rand-1)
Rma=[cos(v1) -sin(v1);sin(v1) cos(v1)]
data=Rma*data
data(1,:)=data(1,:)+2*randn;
data(2,:)=data(2,:)+2*randn;

I can comment this entire section out and it still works do you have any idea what it is used for?

Can you shed any light.

Thank you for your help so far.

[Matt J]

I don't see it anywhere in icp.m. So, I assume it is just used to set up one of the examples.

[John hope]

Hi Matt

Your right it was part of the example and I managed to work out that the code simply offsets the data.

Can i ask, the function takes in the model and data as inputs (as well as other inputs) but i wanted to ask from the code how can you tell which input data set is fixed and which is translated?

I am trying to map one data set onto the other, so i have data set 1 which remains fixed and data set two which is the dataset that floats & maps onto data set 1.

So does model represent the fixed data set and data represent the "floating" data set?

Thanks

[Matt J]

I deduce from this section of the help docunentation

%   OUTPUT:
%
%   R - rotation matrix
%   T - translation vector
%   data2 - matrix with transformed data points,   [ P_1 P_2 ... P_N ]
%
%           data2 = R*data + T

that the "data" input (not the "model") is the data that floats. It is "data" to which the rotation and translation are being applied at the very end.