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microsoft / Recursive-Cascaded-Networks

[ICCV 2019] Recursive Cascaded Networks for Unsupervised Medical Image Registration
https://arxiv.org/abs/1907.12353
MIT License
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Determinant of Jacobian #15

Closed Barnonewdm closed 4 years ago

Barnonewdm commented 4 years ago

I have noticed that the Jacobian Det. is supplied in your code. def jacobian_det(self, flow): _, var = tf.nn.moments(tf.linalg.det(tf.stack([ flow[:, 1:, :-1, :-1] - flow[:, :-1, :-1, :-1] + tf.constant([1, 0, 0], dtype=tf.float32), flow[:, :-1, 1:, :-1] - flow[:, :-1, :-1, :-1] + tf.constant([0, 1, 0], dtype=tf.float32), flow[:, :-1, :-1, 1:] - flow[:, :-1, :-1, :-1] + tf.constant([0, 0, 1], dtype=tf.float32) ], axis=-1)), axes=[1, 2, 3]) return tf.sqrt(var)

My question is why choose the tf.sqrt(var) to represent the Det. of Jacobian. Could you help explain why you choose to compute tf.nn.momnets? The Jacobain Det. should be a map instead of a single value for a given deformation flow.

zsyzzsoft commented 4 years ago

We measure the standard deviation of the Jacobian Det. following the paper "A Deep Learning Framework for Unsupervised Affine and Deformable Image Registration", which quantitatively reflects the smoothness of a deformation field.