Shape description by image moments is a popular topic in image processing. Standard geometric moments are based on a non-orthogonal basis, which has introduced some problems for image reconstruction. Orthogonal moments such as Zernike and Legendre Moments which use orthogonal polynomials have been introduced to overcome this problem. These however are based on continuous polynomials, and are not really suited to digital images processing which is inherently rooted in a discrete domain. Hence, a new type of discrete orthogonal moments, based on Tchebichef polynomials has emerged.

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Source Code Management (SCM) is one of those things that computer scientists and geeks love to talk about, and I think I've just worked out why! When you get a new SCM tool working, and the coin drops - it's awesome! It's like the most impressive Hello World ever. Previously I've used Concurrent Versions System (CVS), which is the only time I've actively collaborated on a software project, and when I started my PhD I used Subversion. I'm a follower of fashion when it comes to SCMs, and as you've probably seen, Git has been spotted all over the internet. So I thought I'd investigate, and this is what I've discovered after using it for around 3 months.

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I've recently been battling with an algorithm, or rather bugs in my implementation of an algorithm, to isolate homogeneous regions in an image. Homogeneous regions? By this we mean areas of identical intensity (the pixel values are the same). As humans we can do this easily; but for a computer, it's harder than it might seem at first... read more...

I need to store some objects in a linked list. Objective-C has a number of container classes NSArray, NSDictionary and NSSet - but I really want a linked list. As I come to Objective-C from a C++ background, I was thinking that this would be where I would use templates, so that I can store any type of in my container. But Objective-C doesn't use templates, it does however have id. read more...

Many spatially distributed data exhibit anisotropic spatial variation, especially when the data are distributed over a large area. The Semivariogram, or commonly (and inaccurately) just variogram is a measure of spatial correlation. It simply plots the semivariance (which is half the variance) of two points separated by a vector h against the magnitude of h. Easy right? Well there is a little bit more to it...

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The method of least squares, or even simply maximum likelihood is one of the more powerful tools available to a statistician. It is powerful because its simplicity means it can be used in a variety of regression problems.

Regression simply means line fitting, and lines are just a graphical way to represent a model, which is the mathematical way to describe the relationship between an independent variable and one or more dependent variables. There is a lot of text on linear straight line fitting, so I’m not going to go into too much detail. I will however briefly discuss the principle behind least squares.

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I do like my graphical front ends; but I am also quite partial the the unix back end of OS X. The AI of SAMRAI stands for Application Infrastructure, which means that it is essentially a lot of code that helps someone wishing to develop a parallel adaptive mesh refinement application do exactly that. Applications are built using the Makefile system; SAMRAI has a configure file, so that it can be incorporated into the developer's own Makefile.

To use Xcode with SAMRAI, it just requires modifiying some build settings, and adding some libraries. Here's what you do...

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I actually started this post around early April, but discovered that my SAMRAI install wasn't actually quite right; which took me a month or so to sort out. Eventually I got SAMRAI and a Level Set Method library working. Only now have I found time to putting some information on the web that some people might find useful.

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Since my standard greedy algorithm works as expected, I made a C++ class from it, using the Cool Image C++ library. This then provides blistering computation of the minimisation process, compared to Python. It does mean I've had to descend into the depths of declaring what sort of variable I want, rather than just its name, but oh well I can't have everything.

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In order to analyse the frequency components of a curve using Fourier we must first represent it mathematically. As we are working with images, a discrete spatial domain, then we have to deal with discretisation.

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Sobel edge detection is a popular technique as it can deliver good results, without excessive computational requirements. The technique utilises the theory of optimal smoothing (Gaussian), and optimal differencing.

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The Hough Transform (HT) is an image processing operation which enables the extraction of shapes, essentially lines from images. The principle is that there are an infinite number of line that pass though any point, each at a different orientation. The HT aims to determine which of those theoretical lines pass though most features in an image.

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Now that I have background monitor working, updating a background image every 60 seconds (a default value), I want to start monitoring the foreground. For these two processes to work at the same time I want to use threads for each one, using the threading module in Python. read more...