ANÁLISIS DE CORRIENTES EN LOS TABLEROS

In this review, sections 3.5 to 3.5.4.4 investigated the medical 2D-3D literature, sub- dividing the algorithms into point based, contour based, surface based and intensity based. The algorithms could also have been classied as video - MR/CT based, or radiograph/uoroscopy - CT based.

Penney provides a thorough comparison of the radiograph/uoroscopy - CT registration algorithms [Penney, 1999]. Two points are important. First, radiograph/uoroscopy images are completely dierent types of images to video images. The former display the

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amount of X-ray radiation passed through an object, the latter, the visible radiation reected o of an object. Secondly, Penney points out the advantages of intensity based algorithms over feature based algorithms. Penney selects an intensity based algorithm on the basis that the intensity based algorithms are more accurate, they avoid a segmen- tation process which may be error prone, and the fact that in 3D-3D volume registration intensity based methods have outperformed feature based methods [West et al., 1997; West et al., 1999]. The intensity based, radiograph - CT registration algorithms reviewed all illustrate the method that intensity based matching can be performed by simulating a 2D image from the 3D CT, and comparing the simulated image with the real radiograph. In each case, similarity measures such as correlation or gradient measures [Lemieux et al., 1994], pattern intensity [Weese et al., 1999], gradient dierence [Penney et al., 1998] and so on are optimised by a multidimensional search strategy. Penney illustrates that the choice of similarity measure must consider the available intensity information that can be matched, and also be robust to spurious information such as interventional stents in the radiograph that will not match any part of a pre-operative CT.

3.6.4.1 Video - MR/CT Registration Algorithms

As with the camera calibration, and pose estimation algorithms, it is dicult to compare the video - MR/CT algorithms. Table 3.1 provides a summary of the main points of each of the reviewed algorithms, and table 3.2 shows the testing procedure or how many times the registration algorithm has been applied.

The degree of automation often determines clinical applicability. This is not considered here in detail, as many of the details are missing from the papers. It is sucient to point out that Edwards, Colchester and Grimson's method are used clinically, the others are not. Grimson's method has been used on 70 patients [Grimson et al., 1998], Edwards' most recent system on 3 patients [Edwards et al., 1999b], and Colchester's system on 6 neurosurgical operations [Colchester et al., 1996]. Edwards' is the only system whose registration accuracy has been compared with bone implanted markers, and the accuracy ranges from 0.5 - 4mm. Furthermore, Edwards' system tracks the patient moving relative to the video cameras, and updates the registration at 1-2 times per second. Grimson and Colchester both use surface matching and cite the mean distance between the two surfaces as a measure of registration performance. This cannot be considered an accurate error metric, but a low distance of 1.6 and

<

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Algorithm Feature Space Similarity Metric Search

Space Search Strategy

Edwards Tracked 3D distance2 _{ext. Direct}

Markers

Betting 2D Contour 5D distance2 _{ext. Modied ICP}

3D Surface

Betting 3D Surfaces 6D distance2 _{ext. Modied ICP}

ext, int.

Colchester 3D Surfaces 3D log distance ext. Decreasing Step Size Grimson 3D Surfaces 3D Gaussian ext. Davidon Fletcher

distance Powell Quasi New-

ton Lavallee 2D Contour 3D Distance2 _{ext. Levenberg}

3D Surface Marquardt

Viola 2D Intensities Mutual ext. Stochastic Gradient

3D Surface Information Descent

Table 3.1: A summary of video-3D algorithms.

Algorithm Images Tests Accuracy Time Hardware

Edwards Clinical Many 0.5-4mm Real

time

Sun,Intergraph

Betting Video/CT 1 0.76 pix 10s DEC Alpha

Phantom 0.17 degrees

X-ray/CT 1 0.79 pix DEC Alpha

Skull 0.7 degrees

Betting 2 Video 1 1.6 mm 50s DEC Alpha

MRI, face

Colchester Clinical Many

<

Sparc IPX

Grimson Clinical Many 1.6mm 120-240s

Viola Video/CT 200 1.34,0.99,11.01mm 35s Sun

Phantom 3.09 degrees Sparc 5

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methods respectively indicates that the registration was probably successful. Grimson's and Colchester's method both require 120 - 180 seconds to re-register if the patient moves.

Both Colchester et al. and Grimson et al. use surface matching and have used their algorithms in clinical situations. Both methods rely on the accuracy of surface recon- struction. Colchester's method projects lines onto a surface. Two video cameras capture images, an edge detection algorithm used, and corresponding points are matched be- tween views. Edge detection and corresponding point matching are known to be dicult problems, that to date are still ongoing research areas. The problem is increased if the surfaces are wet, shiny, and overly textured. For each incorrectly identied edge pixel, the search for correspondences across views increases. Thus it would be better to have an algorithm that does not rely on an edge detection process. Grimson uses a laser scan- ner, which gives a very accurate surface reconstruction. However, laser scanners can be inconvenient to use within a medical environment. It would be better to have a system that does not need a laser.

Betting and Feldmar's paper [Feldmar et al., 1997] simply repeats the results in [Feldmar et al., 1994; Betting and Feldmar, 1995; Betting et al., 1995]. Yet for each of the two algorithms reviewed, only one registration result exists. Furthermore no gold standard is used and the methods only use phantoms. The main problem with using a method such as these is that they require segmentation in both the 2D and 3D images, and also require that an external contour is indeed present in the video images. This will make it dicult to apply to a wide variety of cases.

Viola's method removes the need for segmentation of the 2D image. This is a signicant step in the right direction. However, it has only been tested on skull phantoms. At the very least, further tests need to be done. In addition, it assumes that the surface being viewed is of one material type, and textureless. i.e. It is one smooth colour, reecting light in a consistent manner over the whole surface, subject to lighting conditions. This is in practice not the case. Most surfaces exhibit some level of texture. In addition, in an operating room environment, surfaces become wet, and can be covered in blood. Viola's method may not work well in practical applications.