Unformatted text preview: ure 5.13: An initial incorrect pose. The model has been moved 150 millimeters toward
the camera. Figure 5.14: The nal aligned poses. 121 Paul A. Viola CHAPTER 5. ALIGNMENT EXPERIMENTS Figure 5.15: Ten frames from a video sequence of Ron's head. 122 5.1. ALIGNMENT OF 3D OBJECTS TO VIDEO AI-TR 1548 Figure 5.16: Bumps with Di erent Lighting, and their Edges 5.1.3 Alignment of Curved Surfaces
The third experiment is designed to explore the nature of the information that EMMA alignment uses to detect the correct pose. The previous two experiments, because they are based
on real data, can be di cult to analyze. We would like to determine which component of
the information in the image and model is critical to alignment. For example, it could be the
case that EMMA alignment relies implicitly on intensity edges to match model to image. Or,
it could be the case that the occluding contours of the object are of critical importance.
For this experiment we created a very simple, almost pathological, synthetic example.
123 Paul A. Viola CHAPTER 5. ALIGNMENT EXPERIMENTS Figure 5.17: Target Image, Final Model Pose, and Initial Model Pose
The object is a set of three Gaussian shaped bumps in a at patch of surface. This object in
has no sharp edges and does not have a well de ned occluding contour. Figure 5.16 shows
ten di erent images of this object. Each image uses the same Lambertian re ectance model
but has di erent illumination. Across the top row the light source moves gradually from left
to right. In the second row the light source moves from top to bottom. Even for a simple
Lambertian surface, image variation can be signi cant. Below this we show the output of a
Canny edge detector run on the ten di erent images Canny, 1986. The variation between
the di erent edges extracted is quite striking.
Figure 5.17 shows the target image on the left. Here the bumps are inserted into an in nite
plane. Also shown is a rendered version of a typical nal and initial pose of the model. As in
other experiments the rendered images of the model are made using a particular surface and
lighting scheme; they are for visualization only and play no role in the alignment process.
The black regions of the rendered image lie outside the borders of the model. Notice that
the model's boundaries do not coincide with any discontinuities in the target image. Since
there are neither stable edges nor usable occluding boundaries, we can conclude that EMMA
alignment can proceed using only shading information.
The bumps each have a sigma of 7mm the bump is about 3 sigma or 21mm wide. The
bump height is 20mm. Lying together in the same plane they take up an L shaped region that
is 100mm by 100mm. The true pose is 1000mm away from the camera and perpendicular to
the camera axis. The camera has a viewing angle of 18 degrees. This experiment proceeds
exactly as in the previous three dimensional experiments.
As we did with the skull model we performed an analysis of the reliability of the maxima
of mutual information. These experiments summarized in Table 5.4.
124 5.1. ALIGNMENT OF 3D OBJECTS TO VIDEO X 4T
Y mm Z 4 10 10 25 30
15 15 25 20
20 20 25 20 X AI-TR 1548 INITIAL Y Z j 4 j mm
5.21 5.82 19.97 15.41
8.75 8.95 14.61 9.15
11.72 11.07 13.85 9.22 X
.65 FINAL SUCCESS mm
80 Y Z j 4 j Table 5.4: Curved Surface Alignment Data 125 5.68
3.12 Paul A. Viola CHAPTER 5. ALIGNMENT EXPERIMENTS 5.2 Medical Registration Experiments
EMMA alignment of three dimensional objects relies on the fact that the image is a function
of the model and the lighting. It is not necessary that we know the exact nature of this
function. In medical imaging we are faced with a di erent though related task. We are given
two di erent observations of the same object. For example we may be given a Computed
Tomography CT scan and Magnetic Resonance Image MRI of the same patient. Two scans
are often obtained because neither gives perfect information about the patient. CT is good
at nding bone. MRI is good for distinguishing soft tissue. These measurements are taken at
di erent times with di erent machines. A clinician that would like to have information about
bone and soft tissue must integrate the two scans into a single self-consistent picture. Once
this is done the spatial relationships between structures in the two di erent scans become
apparent. For example the distance between a tumor and a bone can be measured.
In Chapter 4 we argued that EMMA alignment should be able to align two signals
whenever there is mutual information between them. In this experiment two di erent MR
images of the same head will be aligned see Figure 5.18. These images comprise the proton
density and T2-weighted images of a double-echo MR scan. We have chosen these two MR
scans for two reasons: 1 it is clear that the two images share a great deal of information,
while they are not identical; and 2 since they are taken simultaneously the correct alignment should be close to the identity transformation. Because we know ground truth, we can
evaluate the accuracy of the EMMA alignmen...
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- Spring '10
- The Land, Probability distribution, Probability theory, probability density function, Mutual Information, Paul A. Viola