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## Smoothing 2D Contours Using Local Regression Lines

version 1.2 (3.84 KB) by

This submission contains both the implementation and the test function for 2D contour smoothing.

Updated

A contour of a 2D region is defined by an ordered set of points where the neighboring elements contain the neighboring points. Such representation can be obtained with many techniques such as boundary tracing and chain codes. (In a simple 2D point set or a curve the points do not have to lie in a specific order.)

The contour smoothing is done by projecting all the contour points onto the local regression line. For each point, N neighboring points which lie on the contour are sampled on each side and a local regression line is computed. Then the current point is projected on this line. Applying this algorithm to all the points smooths the contour and in a way brings the points closer. 2N+1 is the number of total points contributing to the computation of the local regression line. The higher the number of points, the smoother the curve.

Because of the linear nature of fitting, when too much smoothing is desired, the algorithm loses important features such as corners, and gets confused in such critical regions. This in a way is a wrong over-smoothing. A way to be less prone to such errors is to use gaussian weighted least squares fit. For this purpose I use Andrey Sokolov's line fitting. Here is the link:
http://www.mathworks.com/matlabcentral/fileexchange/28894-weighted-orthogonal-least-squares

In the test code, a contour is obtained using chain codes (bwtraceboundary) and smoothed. The example is taken from a real application

Benjamin Busam

Lucy Robinson

Tolga Birdal

### Tolga Birdal (view profile)

Normally, the binary region is assumed to be filled, so that MATLAB's trace methods would work. However, it occurs to me that the problem is not in tracing, but MATLAB cannot locate the initial point to begin trace. This might be due to the mis-selection of initial direction. Can you send me your data?

Does the binary input need to have its objects with boundries only or the object should be completely 1.
In my case it gives me this error:
Attempted to access contour(:,1); index out of bounds because size(contour)=[0,0].

Error in test_smooth_contours (line 39)
[Ys Xs]=smooth_contours(contour(:,1), contour(:,2), 21);

Paul Doliotis

Zannatul

Zannatul

Henry Zhu

### Henry Zhu (view profile)

 20 Jul 2011 1.2 Description updated 21 Mar 2011 1.1 Now uses Andrey Sokolov's Weighted Orthogonal Least Squares fit, with gaussian weighting. This is smoother, more robust and less prone to sudden changes such as corners. (If gaussian weighting is not used, it's also faster).
##### MATLAB Release
MATLAB 7.9 (R2009b)