http://inperc.com/blog2/2007/10/20/lengths-of-digital-curves-continued/ Computer vision, image analysis, and related mathematics Thu, 17 Feb 2011 13:25:51 +0000 hourly 1 http://wordpress.org/?v=3.1.3 http://inperc.com/blog2/2007/10/20/lengths-of-digital-curves-continued/comment-page-1/#comment-33 Computer Vision for Dummies » Connectivity (or Lengths of Digital Curves, part 6) Fri, 07 Dec 2007 14:22:21 +0000 http://inperc.com/blog2/2007/10/20/lengths-of-digital-curves-continued/#comment-33 [...] Yes, part 6! I thought I was done with the topic (Part 1, Part 2, Part 3,…), but a couple of days ago I ran into this blog post: General connectivity (MATLAB Central) . The issue is connectivity in digital images: 4-connectivity, 8-connectivity, and other “connectivities”. The issue (adjacency of pixels) is discussed in the wiki. When I wrote this article though I did not realize that the topic is connected to measuring lengths of curves. Indeed, the 8-connectivity produces curves that go only horizontally or vertically while the 4-connectivity allows diagonal edges as well. In the post the curves appear as “perimeters” of objects. More accurately, they should be called contours or boundaries of objects as the perimeter is mathematically the length of the boundary (that’s where “meter” comes from). But bwperim is the name of the standard MATLAB command for finding the boundary and we will have to live with that… [...] [...] Yes, part 6! I thought I was done with the topic (Part 1, Part 2, Part 3,…), but a couple of days ago I ran into this blog post: General connectivity (MATLAB Central) . The issue is connectivity in digital images: 4-connectivity, 8-connectivity, and other “connectivities”. The issue (adjacency of pixels) is discussed in the wiki. When I wrote this article though I did not realize that the topic is connected to measuring lengths of curves. Indeed, the 8-connectivity produces curves that go only horizontally or vertically while the 4-connectivity allows diagonal edges as well. In the post the curves appear as “perimeters” of objects. More accurately, they should be called contours or boundaries of objects as the perimeter is mathematically the length of the boundary (that’s where “meter” comes from). But bwperim is the name of the standard MATLAB command for finding the boundary and we will have to live with that… [...]

]]> http://inperc.com/blog2/2007/10/20/lengths-of-digital-curves-continued/comment-page-1/#comment-21 Computer Vision for Dummies » Lengths of digital curves, part 5 Tue, 13 Nov 2007 15:36:42 +0000 http://inperc.com/blog2/2007/10/20/lengths-of-digital-curves-continued/#comment-21 [...] Here is how it happened. The algorithm for roundness computes the perimeter first. More precisely, it computes the “adjusted” perimeter. The reason is that the perimeter computed as the number of steps in the curve depends on the orientation of the curve with respect to the grid. This “first degree approximation” produces the same roundness for a square and a 5×1 rectangle. To compute the better adjusted perimeter we use the “second degree approximation” that takes into account both the perimeter and the curvature (number of turns). Some error is still there but the results were supposed to be much better. And they were until I tried a diagonally oriented square. The roundness was way off! [...] [...] Here is how it happened. The algorithm for roundness computes the perimeter first. More precisely, it computes the “adjusted” perimeter. The reason is that the perimeter computed as the number of steps in the curve depends on the orientation of the curve with respect to the grid. This “first degree approximation” produces the same roundness for a square and a 5×1 rectangle. To compute the better adjusted perimeter we use the “second degree approximation” that takes into account both the perimeter and the curvature (number of turns). Some error is still there but the results were supposed to be much better. And they were until I tried a diagonally oriented square. The roundness was way off! [...]

]]> http://inperc.com/blog2/2007/10/20/lengths-of-digital-curves-continued/comment-page-1/#comment-16 Computer Vision for Dummies » Lengths of digital curves, part 3 Sat, 27 Oct 2007 20:33:06 +0000 http://inperc.com/blog2/2007/10/20/lengths-of-digital-curves-continued/#comment-16 [...] Recall that in the previous posts we discussed what happens if one computes the length of a curve in a digital image as the total sum of distances between consecutive points. The conclusion was that using the length computed this way to evaluate the shapes of objects leads to disastrous results. [...] [...] Recall that in the previous posts we discussed what happens if one computes the length of a curve in a digital image as the total sum of distances between consecutive points. The conclusion was that using the length computed this way to evaluate the shapes of objects leads to disastrous results. [...]

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