122 The acquisition frame rate ranged from 25 to 30 frames/s. All the recordings were converted to audio video interleave (AVI) format for further analysis. Due to motion artifacts during insertion and positioning of the probe in the uterine cavity as well as during its removal, the time length for all 2-D recordings was shortened to 3 min by cropping a certain part of the recording in the beginning and at the end. B. Ultrasound Speckle Tracking US speckle is caused by the interference of the backscatter US waves received by the transducer. Tissue forms a unique speckle pattern that can be tracked over time. Therefore, tissue motion can be assessed by tracking the movement of the speckle pattern. The highest endometrial wave velocity is less than 2 mm/s [10]. Therefore, with an acquisition frame rate and pixel size equal to 30 Hz and 0.065 mm, respectively, uterine motion between subsequent frames was smaller than one pixel. To deal with such subpixel motion and provide accurate tracking results, OF was employed to perform speckle tracking in this study. With I being the intensity of a certain pixel, the pixel velocities in the x - and y -directions, vx and vy , are thus represented by the intensity gradients in the spatial (x,y ) and temporal (t) domains according to $_& '(/'& +$_+ '(/'+ +'(/', =0 To solve the above ill-conditioned equation, Lukas and Kanade [22] proposed to estimate the motion of a block instead of a pixel under the assumption of constant flow within the block. The velocities in both directions are then obtained by least square estimation. After that, the pixel location in the target frame is updated according to the estimated velocities. The accuracy of OF can be further improved by applying an iterative refinement approach under the assumption of small motion [16]. In this study, OF was first applied to track the motion of a selected speckle pattern between the reference frame and the target frame. Based on an initial estimation v1 , the target frame was warped by the 2-D interpolation. In this way, the movement of the speckle pattern was partly retrieved between the reference and the target frames. In the following second iteration, a new estimation of residual motion, v2 , was derived between the reference and the warped target frames. This process was applied iteratively until the residual motion vn converged to a very small value or it reached the maximum number of
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