Comments on: Connectivity (or Lengths of Digital Curves, part 6) http://inperc.com/blog2/2007/11/30/connectivity-or-lengths-of-digital-curves-part-6/ Computer vision and image analysis for newcomers Wed, 27 Jan 2010 21:13:46 +0000 http://wordpress.org/?v=2.9.2 hourly 1 By: Administrator http://inperc.com/blog2/2007/11/30/connectivity-or-lengths-of-digital-curves-part-6/comment-page-1/#comment-35 Administrator Sat, 08 Dec 2007 21:37:24 +0000 http://inperc.com/blog2/2007/11/30/connectivity-or-lengths-of-digital-curves-part-6/#comment-35 Thanks for the feedback, Steve. I like the definition of a matrix as "[a] rectangular array of numeric or algebraic quantities subject to mathematical operations." However, it seems ambiguous. Is it “quantities subject to mathematical operations” or is it “array... subject to mathematical operations”? Some prefer the former while I think it’s (or should be) the latter. I also feel that these operations should include multiplication. For example, (matrix) multiplication of images is meaningless. I admit I tend to behave a bit territorial when I see mathematical terms are used loosely. Unfortunately, it happens way too often. I cringe every time I hear about “exponential growth”... Thanks for the feedback, Steve.

I like the definition of a matrix as “[a] rectangular array of numeric or algebraic quantities subject to mathematical operations.” However, it seems ambiguous. Is it “quantities subject to mathematical operations” or is it “array… subject to mathematical operations”? Some prefer the former while I think it’s (or should be) the latter. I also feel that these operations should include multiplication. For example, (matrix) multiplication of images is meaningless.

I admit I tend to behave a bit territorial when I see mathematical terms are used loosely. Unfortunately, it happens way too often. I cringe every time I hear about “exponential growth”…

]]> By: Steve Eddins http://inperc.com/blog2/2007/11/30/connectivity-or-lengths-of-digital-curves-part-6/comment-page-1/#comment-34 Steve Eddins Sat, 08 Dec 2007 01:19:39 +0000 http://inperc.com/blog2/2007/11/30/connectivity-or-lengths-of-digital-curves-part-6/#comment-34 Hi, MATLAB is widely used for algorithm development and prototyping in the area of image processing. Algorithm developers need to be aware of varying definitions of connectivity, and their tools need to provide appropriate choices. Defining neighbor adjacencies applies to many different image processing algorithms; bwperim was merely the example I chose to illustrate. It's true that bwperim does not compute the perimeter, and I understand why you might not like the name. Rather, it computes the set of digital image pixels that lie along the boundary, or perimeter, of a connected set of foreground pixels. Connectivity comes into play in deciding which pixels are on the boundary. Pixels are judged to be on the boundary if they are adjacent to a background pixel. Adjacency depends on the connectivity definition in use. I agree with you that this is not especially relevant to estimating the perimeter of the "real" object, but that is not bwperim's purpose. Finally, I think your definition of matrix is unnecessarily restrictive. American Heritage, for example, gives the mathematics definition of matrix as "A rectangular array of numeric or algebraic quantities subject to mathematical operations." A table is "An orderly arrangement of data, especially one in which the data are arranged in columns and rows in an essentially rectangular form." Either term seems to apply. Given my own background in discrete systems and signals, I'd really prefer something like "two-dimensional sequence," but since I work in MATLAB, "matrix" is very convenient to use and I see no definition-based reason not to use it. Best regards, Steve Hi,

MATLAB is widely used for algorithm development and prototyping in the area of image processing. Algorithm developers need to be aware of varying definitions of connectivity, and their tools need to provide appropriate choices. Defining neighbor adjacencies applies to many different image processing algorithms; bwperim was merely the example I chose to illustrate.

It’s true that bwperim does not compute the perimeter, and I understand why you might not like the name. Rather, it computes the set of digital image pixels that lie along the boundary, or perimeter, of a connected set of foreground pixels. Connectivity comes into play in deciding which pixels are on the boundary. Pixels are judged to be on the boundary if they are adjacent to a background pixel. Adjacency depends on the connectivity definition in use. I agree with you that this is not especially relevant to estimating the perimeter of the “real” object, but that is not bwperim’s purpose.

Finally, I think your definition of matrix is unnecessarily restrictive. American Heritage, for example, gives the mathematics definition of matrix as “A rectangular array of numeric or algebraic quantities subject to mathematical operations.” A table is “An orderly arrangement of data, especially one in which the data are arranged in columns and rows in an essentially rectangular form.” Either term seems to apply. Given my own background in discrete systems and signals, I’d really prefer something like “two-dimensional sequence,” but since I work in MATLAB, “matrix” is very convenient to use and I see no definition-based reason not to use it.

Best regards,

Steve

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