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Wednesday, November 30, 2011

Complexity and vessel tracking

I know that it sounds cliche, but sometimes the most important part of working through the solution to a problem is to stop thinking about the problem in the context that is familiar to you.  I have been working for the past couple of weeks on expanding the scope of my aortoiliac tracking algorithms to account for the various morphologies that the bifurcation and iliacs can take.  The fundamental problem is that you only have a general idea of where the bifurcation happens and where the iliacs are going.  I was walking around the RSNA vendor area and saw a couple of systems that supposedly do centerline extraction for you, but the one unifying aspect of all of those studies is that they are perfect angiograms in normal patients.  It is my opinion that there is little benefit in being able to segment a normal study.
Every time I write an algorithm, I end up with results that are always imperfect.  Specifically, if I take the fundamental algorithms and boil it down to a handful of parameters that control the functionality, the result is that that the segmetation will never work for all possible morphologies and variations that can occur in clinical practice.  Every time the parameters are tweaked, the result across the 128 or so studies that I am training against begins to vary to some degree.  I judge the robustness of an algorithm in terms of whether or not this variability prevent successful tracking. 
In terms of optimization routines, the basic issue is whether or not the changes in parameters alters the parametric space in such a ways that it prevents the desired extrema (assumed to be the global extrema) from being achieved.  In my opinion, a good algorithm is one that successfully tracks >90% of the iliac vessels that it attempts. 
It has been creeping up in the back of my mind over the past couple of months that what I am actually dealing with is the sensitivity to inital conditions encountered in non-linear dynamics.  Minor alterations in the parameters can send the algorithm into undesired areas like tracking the pelvis as a vessel or abruptly stopping in the middle of a vessel.  Since I have to assume that any and all possible criteria that I create for the tracking algorithm will be violated, I am left with a seemingly intractable problem.  More specifically, there is no one set of algorithms or parameters that can linearly track an arbitrary vessel with variable path and contrast opacification.  More and more though I have come to realize that what I should actually be doing is searching for the attractors that underlie the seemingly chaotic path that the algorithm can take. 
Though I have not philosophically been doing this, the aortic tracking algorithm is such a means of finding the chaotic attractor in the parametric space that contains path, density, and continuity of the aorta.  Long ago i accepted that no matter how good my algorithm is, there is always a chance that the aortic tracking would go astray.  At the time, I was in the philosophical mindset of something between game theory and swarm logic where I created millions of independent elements that were allowed to progress subsequently whittled down the results until some cluster of results were reached that had a high probability of being correct (i.e. within the aorta).  At that point, rather than trying to select one, I use some basic statistics to find the underlying common average path.  It turns out that if you create enough element in your swarm and have reasonably good selection criteria, it is possible to track nearly any aorta with even a trace amount of contrast (>100 HU absolute density, which is really only about 25 HU above unenhanced blood).
The next issue is determining how much computational time I am willing to commit to finding the iliac attractors since the algorithm as it stands right now can successfully track all but the extremes of vessel opacification.  Since it is getting late and I have to be at some refresher courses in the morning, I will think about this some more and get back to you.

2 comments:

Unkonwn said...

تقدم ماستر تك احدث مكن تعبئة وتغليف باسعار منافسة في الاسواق المصرية والمحلية
حيث تقوم الشركة بتقديم الدعم والصيانة المستمرة لها

دكتور تجميل said...

قد تتميز بعض ملامح الجمال الشرقية وتختلف عن صورة الجمال الغربي المنطبعة في أذهاننا، لكن النتيجة النهائية هي أن الجميع يبحثون عما يزيد من وسامتهم وجمالهم، أو على الأقل ما يحافظ على رونق الشباب الذي يحفظ لهذا الجمال حيويته ونضارته. عيادات عمليات التجميل في مصر أحد أهم طرق السعي وراء الجمال أو وراء الحفاظ عليه لأطول فترة ممكنة. فتعالوا معنا في رحلة قصيرة في عالم عمليات التجميل.