2D slices of Fk(x)

In the experiment of Corpus Callosum border segmentation, the model C=(tx, ty, theta, s, b1, b2, b3, b4, b5, b6), where tx and ty is the translation, theta is the rotation, s is the scale, b1...b6 are the shape parameters. We normalized the parameters to make sure that a unit change in a specific parameter causes the same amount of shape variation in image space.

We assume the initial error of the pose is [20 20 pi/9 0.2]. The initial error of the shape parameters is 3*sqrt(lambda).  Please refer to section 5.1 in the paper for more details.

We show the trained Fk(x)'s on a testing data. The testing data is:

 

Because Fk(x)'s are high dimensional functions, we plotted the 2D slices by varying two chosen parameters of the model C in the feasible region while fixing the remaining parameters as the ground truth. In the paper, we showed the 2D slices of 1st and 5th dimension in Figure (7).

We trained 3 levels of regressors. In each video, the top one is F1(x). The bottom left is F2(x). The bottom right is F3(x).

The overlay black mesh-grids are the target density functions qk(C|I). The color meshes are learned regressors Fk(x).

The slices of 1st and 2nd dimension

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The slices of 1st and 3rd dimension

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The slices of 1st and 4th dimension

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The slices of 1st and 5th dimension

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The slices of 1st and 7th dimension

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The slices of 1st and 10th dimension

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The slices of 3rd and 4th dimension

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The slices of 3rd and 8th dimension

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The slices of 4th and 7th dimension

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The slices of 5th and 10th dimension

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The slices of 7th and 8th dimension

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The slices of 7th and 10th dimension

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The slices of 9th and 10th dimension

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