Motion model
The addressed problem is estimating the 2-D dense motion field between a pair of images. In many application (see the examples above), complex displacements may occur. In order to consider their complexity, we propose to use a bilinear motion model for controlling the local mesh deformation.
Example of displacement using bilinear model:
Application examples
Ultrasound elastography, flow imaging, heart motion estimation.
Motion estimation
The eight parameters of the bilinear model are locally estimated using an iterative approach (see Basarab et al.
The main steps of estimating the bilinear model for a rectangular region on the reference image are:
Iteration 1:
1) Consider 4 rectangular blocks centered on its corners. The blocks are joined in the current node (the center of the region).
2) Estimate by classical block matching (BM) the translation of these four blocks.
3) Two linear systems of four 4 equations with four unknowns allow us to calculate the 8 bilinear parameters.
Iteration 2:
4) Deform locally the reference image taken into account the estimated model.
5) Re-consider the four blocks.
6) Estimate by BM their translations.
7) Re-calculate the 8 bilinear parameters.
…
Results
Motion estimation results with two applications are shown hereafter.
Motion estimation with B-mode ultrasound images - application to flow imaging
(Basa-07, ICIP)
Mesh deformation Lateral shear (bu parameter)
Motion estimation with RF ultrasound images - application to ultrasound elastography
(Basa-08, MEDIA)
(a) Deformed mesh superimposed to the ultrasound B-mode image corresponding to a thyroid with a malignant tumor.
(b) Estimated thyroid tumor cartography superimposed to the ultrasound B-mode image (Th - thyroid, Tm - tumor). The contours of the thyroid gland and of the tumor were manually outlined on the ultrasound images by the radiologist who performed the examination.