Validation of algorithms

Outcome measure

To be able to compare manual and semi-automatic overlay, an outcome measure needs to be defined. We have chosen to hand-pick a set of points on the images that we can confirm are the same in both images, so that if the transformation of one image into the other coordinate frame is done, the distance between the hand-picked points in the fixed image and the transformed image will be the local measure of how well the two images match.

For each of the image pairs that are used for the validation, 16 corresponding control points are manually selected by the researcher as uniformly as possible on the cortex. The mean distance or error per control point pairµD then acts as a goodness-of-fit parameter with which

registrations can be evaluated; this is the outcome measure. Mathematically, µD can be expressed as:

µD =

P16

n=1||mn−fn||

16 (3.3)

where mn corresponds to the nth point of the 16 outcome control points in the transformed or

“moving” image (this being Iel orIpost) and fn the nth point of the outcome control points in

the fixed image (Ipre). For each pair of points, the euclidean distance is computed between the

points and all of the distances are meaned.

ThisµD will be expressed in pixels and in millimeters. The conversion to millimeters is done by

using the electrode grids on theIel images as a reference; the interelectrode distance is exactly

1 cm. Up to nine electrodes were pinpointed in every electrode picture by the researcher and the mean distance of those nine electrodes measured (pairwise, along the lines of the grid so as not to measure a diagonal).

Clinician validation

Three clinicians performed both the manual overlay task and a semi-automated overlay task for all 20 patients. Two image pairs were assigned for registration per task: the Ipre−Iel pair

and the Ipre −Ipost pair. All images are then transformed to the coordinate system of the Ipre

image.

After these manual and semi-automatic overlays, the mean error µD is computed per task and

patient. The time spent by the clinicians for each task is also recorded.

Effect of collinearity and point spread

When performing the semi-automatic overlay, users are free to choose the control points where they want on the cortex. They are instructed to not place them collinearly, and spread them

(a) (b)

(c) (d)

Figure 3.2: (a)From top to bottom, these are theIpre,Iel andIpost images for patient EP 03. These photos

are taken at the start of surgery but after trepanation, after placement of an electrode grid, and after resection respectively. (b) For the same patient, this is a fused view of the Ipre and Iel images with Ipre shaded in

green,Iel in magenta and areas with similar colors in grayscale. Manually, 16 points have been selected by the

researcher on both images, and these points are connected with red lines, making visible the initial mismatch between the two pictures. (c) The same fused view, but after the manual task by clinician 2. The errors between the same 16 points are now shown in green. (d)The same image pair after the semi-automatic task of clinician 2. Errors are shown in purple and the three control points that have been clicked in blue. Naturally, because pairs of three points are fitted, those control points have zero error, as the algorithm fitted the images to minimize those errors. If more than three points are fitted, this zero error for the control points is not guaranteed.

(a)

(b)

Figure 3.3: (a) Example of an overlay task in GIMP. Here, the electrode image is being manipulated to be in the same coordinate frame as the underlying clean brain image. The operations that are being used are translation, rotation, (ratio-independent) scaling and shearing. (b) Example of a semi-automatic task of the same image pair in MATLAB. The user selects a minimum of three control points that correspond between the two images, so that a registration algorithm can then put the two images in the same coordinate frame.

out as much as possible while still placing them on the brain.

To measure the effect of these two things, a collinearity measurecolland the area of the triangle

A formed by the control points will be computed. If we label the lengths of the three edges of the triangle as e1, e2 and e3, the collinearity is defined like this:

coll= 2ea−(eb+ec)

ea

(3.4)

ea= max

i ei ∀ i ∈ {1,2,3} (3.5)

where ea is the length of the largest edge of the triangle and eb and ec are the lengths of the

other two. This collinearity measure will vary between 0 and 1; it will be 1 if eb +ec = ea

(when the three vertices of the triangle are aligned), and 1 if ea = eb = ec, when the control

points form an equilateral triangle.

The area of the triangle is computed with the MATLAB function polyarea.

Non-clinician validation

In addition to the validation by clinician, five non-clinicians are also asked to perform the manual and semi-automatic overlay on three patients in the same way, and the result compared with clinician performance.

Because of time constraints, three patients were chosen for the non-clinicians to perform the manual and semi-automatic overlay on, namely EP 02, EP 04 and EP 06. These values will be compared with the values of the clinicians for these three patients. Non-clinicians were students of industrial design, civil engineering and physics recruited at the TU Delft university; none of these non-clinicians had a medical background.

3.3

Results