| skel - skeletonization, thinning, Medial Axis Transform |
[skl,dt,lbl] = skel(img [,side, algorithm]) |
| img |
| Binary image containing one or more binary shapes. (foreground == 1, background == 0), One-pixel-wide regions are ignored (temporary limitation). |
| side |
| interior if only internal skeleton is desired (DEFAULT); |
| exterior if only external skeleton is desired; |
| both if the background and foreground skeleton must be computed at the same time. |
| algorithm |
| fast euclidean (DEFAULT) will perform a fast O(n) algorithm using the euclidean metric. For large and thick shapes, there may be a few small errors, which are dispensible for most practical applications. |
| exact euclidean will perform an exact euclidean algorithm that is very much slower. |
| skl |
| The multiscale skeleton image. This is a grayscale image, which may be thresholded to yield a skeleton with varying levels of detail. The greater the threshold, the cleaner is the skeleton. A threshold level of 5 will give a usual skeleton similar to the one obtained by popular thinning methods. |
| dt |
| The euclidean distance transform of the image. It has the squared euclidean distances of any point of the image to the object. |
| lbl |
| Label image. This is the discrete Voronoi Diagram of the boundary pixels of the considered object. Is is a grayscale image indicating the region of influence of each boundary pixel. |
| Function skel performs skeletonization (thinning) of a binary object. The resulting medial axis is multi-scale, meaning that it can be progressively pruned to eliminate detail. This pruning is done by thresholding the output skeleton image. |
| The algorithm computes skeletons that are guaranteed to be connected over all scales of simplification. The skeletons are computed using the euclidean metric. This has the advantage to produce high-quality, isotropic and well-centered skeletons in the shape. However the exact algorithm is computationally intensive. |
| The radius of the maximal balls associated with the skeleton points are stored in the distance transform output image. |
initial_dir = PWD;
chdir (SIPDIR + 'images');
xset('auto clear', 'on');
im=gray_imread('escher.png');
imshow(im,2);
[skl,dt,vor] = skel(im);
// Fine detail
sklt = (skl >= 5);
imshow(im+sklt,[]);
// Less detail
sklt = (skl >= 20);
imshow(im+sklt,[]);
// The Distance Transform
imshow(sqrt(dt),[]);
// The Influence/Voronoi diagram of each boundary pixel
imshow(vor+1,rand(maxi(vor)+1,3)); // each region maps to a random color
// Let's see if computation is really fast
big = mogrify(im,['-sample','1000x']);
size(big)
skl = skel(big);
imshow(big + (skl >= 50),[]);
xset('auto clear', 'off');
chdir(initial_dir);
|
| For the fast euclidean algorithm: "Multiscale Skeletons by Image Foresting Transform and its Application to Neuromorphometry", A.X. Falcao, L. da F. Costa, B.S. da Cunha, Pattern Recognition, 2002. |
| For the exact euclidean algorithm: |
| "Multiresolution shape representation without border shifting", Costa, LF and Estrozi, Electronics Letters, no. 21, vol. 35, pp. 1829-1830, 1999. |
| "Shape Analysis and Classification", L. da F. Costa and R.M. Cesar Jr., CRC Press. |
| Ricardo Fabbri <rfabbri@if.sc.usp.br> |
| The latest version of the Scilab Image Processing toolbox can be found at |
| http://siptoolbox.sourceforge.net |
| thin, reconstruction (not done yet...) |