Doubts over saddle point locations

I set off to another glorified week when I intend to investigate the possibility implementing an automatic pulmonary vein detector. From the segmented atrium I wish to locate the pulmonary vein drainage ostium automatically so that their diameters can be calculated by some interactive means.

I had doubts over whether the saddle point algorithm was correctly detemrining the points on the image. A thorough close-examination of the algorithm and after some gruesome hours of analyzing the basic component maps I have come to the conclusion that the saddle point algorithm is working fine. I may not be color coding the BC maps correctly at times, so when the saddle points are overlaid over a color-coded BC map, they appear to be located over points which are not boundaries between two adjacent components. This is the case since the color mapper needs to be fine-tuned and by default neighboring components sometime get the same color.

The tube ride today was very instrumental allowing me to finally think of a way the automatic PV drainage detection can be done. I have noticed that the atrium is nicely subidivided at the ostiums for most of the cases. The only thing that needs to be done is to characterize these ostiums interms of the subdivisions or perhaps saddle point diameters.

MIUA paper

It has been a hectic week working on my first ever conference paper. The Medical Imaging Understanding and Analysis 2007 conference is to be held in Wales this year, and I am looking forward to visiting the place. Here is my paper on left atrium segmentation.

Basic component subdivision is random

Today I investigated how subdivision occurs near the pulmonary artery and pulmonary vein intersections. Intersections are caused by partial volume effects. I managed to analyse two datasets. In both datasets I have determined that the subdivision process is fairly random (although I still believe that to some extent it depends on the shape, but then again the shape is quite random near PV+PA intersections). The above image is a slice through the MRI showing the different subdivsions (color coded, i.e. a different color for each subdivision). The marked region within the image shows a pulmonary vein what is part of the left atrium but becomes part of the pulmonary artery due to the way that region was subdivided.

Ideally I would have liked the region marked to be a separate subdivision so that it could be merged in with the subdivisions at the atrium. This creates a massive problem where these subdivsions no longer make sense. Previously I have been under the impression that the left atrium would be uniformly subdivided. Thoughts on which directions to proceed: 1. Use a different neighborhood for picking local maximums (currently we use a 26-neighborhood).

Automatic segmentation

I have passed my MPhil to PhD transfer. Transfers can take a long time: it took me about 2 months to prepare the report and compile results. It is a good idea to write up the transfer report in thesis style keeping in mind that some parts of the transfer report can be recycled to be used in the final thesis.

It is now possible to automatically segment the left atrium using a subdivision and merging algorithm. The atrium is subdivided into disjoint components using some geometric means. These components are then automatically merged using a criterion defined on any two neighboring components. The merging criterion is defined using the notion of a narrowing. Any two neighboring components separated by a narrowing are not allowed to merge. This uses the assumption that the atrium is attached to neighboring structures only through narrow vessels. Allowing the merging to start from the center of the atrium, and stopping the merging at these narrowing can segment the atrium. However, we report that this assumption is not entirely correct. Narrowings can occur within the atrium itself: we have encountered a patient case where the left atrium opens into a pulmonary vein through a narrowing.

Seen above is a surface reconstruction of a left atrium segmented using the automatic scheme described above. A unusual narrowing within the ostium of a pulmonary vein caused the segmentation to miss the pulmonary vein completely. This was corrected by setting a second seed point at the center of the missed vein, and automatically segmenting and merging it with the original segmentation.

Above is my cartoon representation of a left atrium and its surrounding structures. Assume the blue tubular structure to be the ascending aorta, and the green structure to be the pulmonary artery. The left atrium is drawn in red. Using the narrowing scheme we described above, it still becomes difficult to separate the atrium from the pulmonary artery. The artery and the pulmonary veins touch as seen in the figure, and this is due to the partial volume effect. There is no genuine narrowing at these points (where the vein intersects the artery). As a result we have the system thinking that components on either side of this touching point should be merged - causing segmentation to leak into the artery.

We are looking at different ways to overcome this problem. It may be useful to compute the medial axis transform of the vessels. Vessles which touch due to partial volume effects may not have their medial axes touching. We could perhaps exploit this feature and detect where partial volume effect caused non-mergeable components to be merged.

Acknowledgements: The automatic segmentation technique was adopted from John et. al. 2005.