  Displacement estimation is a critical step of virtually all Ultrasound
Elastography (USE) techniques. Two main features make this task unique compared
to the general optical flow problem: the high-frequency nature of ultrasound
radio-frequency (RF) data and the governing laws of physics on the displacement
field. Recently, the architecture of the optical flow networks has been
modified to be able to use RF data. Also, semi-supervised and unsupervised
techniques have been employed for USE by considering prior knowledge of
displacement continuity in the form of the first- and second-derivative
regularizers. Despite these attempts, no work has considered the tissue
compression pattern, and displacements in axial and lateral directions have
been assumed to be independent. However, tissue motion pattern is governed by
laws of physics in USE, rendering the axial and the lateral displacements
highly correlated. In this paper, we propose Physically Inspired ConsTraint for
Unsupervised Regularized Elastography (PICTURE), where we impose constraints on
the Poisson's ratio to improve lateral displacement estimates. Experiments on
phantom and in vivo data show that PICTURE substantially improves the quality
of the lateral displacement estimation.
