Outline your hand with splines (Matlab)

Question

I'm trying to write a script so that one can put his hand on the screen, click a few points with ginput, and have matlab generate an outline of the persons hand using splines. However, I'm quite unsure how you can have splines connect points that result from your clicks, as they of course are described by some sort of parametrization. How can you use the spline command built into matlab when the points aren't supposed to be connected 'from left to right'?

The code I have so far is not much, it just makes a box and lets you click some points

FigHandle = figure('Position', [15,15, 1500, 1500]);
rectangle('Position',[0,0,40,40])
daspect([1,1,1])
[x,y] = ginput;

So I suppose my question is really what to do with x and y so that you can spline them in such a way that they are connected 'chronologically'. (And, in the end, connecting the last one to the first one)

Answer 1

look into function cscvn

curve = cscvn(points) 

returns a parametric variational, or natural, cubic spline curve (in ppform) passing through the given sequence points(:j), j = 1:end.

An excellent example here: http://www.mathworks.com/help/curvefit/examples/constructing-spline-curves-in-2d-and-3d.html

Answer 2

I've found an alternative for using the cscvn function.

Using a semi-arclength parametrisation, I can create the spline from the arrays x and y as follows:

diffx = diff(x);
diffy = diff(y);
t = zeros(1,length(x)-1);
for n = 1:length(x)-1 
    t(n+1) = t(n) + sqrt(diffx(n).^2+diffy(n).^2);
end
tj = linspace(t(1),t(end),300);

xj = interp1(t,x,tj,'spline');
yj = interp1(t,y,tj,'spline');
plot(x,y,'b.',xj,yj,'r-')

This creates pretty decent outlines.

What this does is use the fact that a curve in the plane can be approximated by connecting a finite number of points on the curve using line segments to create a polygonal path. Using this we can parametrize the points (x,y) in terms of t. As we only have a few points to create t from, we create more by adding linearly spaced points in between. Using the function interp1, we then find the intermediate values of x and y that correspond to these linearly spaced t, ti.

Answer 3

Here is an example of how to do it using linear interpolation: Interpolating trajectory from unsorted array of 2D points where order matters. This should get you to the same result as plot(x,y).

The idea in that post is to loop through each consecutive pair of points and interpolate between just those points. You might be able to adapt this to work with splines, you need to give it 4 points each time though which could cause problems since they could double back.

To connect the start and end though just do this before interpolating:

x(end+1) = x(1);
y(end+1) = y(1);