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OF(optical flow) Computation is widely used in image registration, motion analyzing, and motion object detection. This paper employs OF computation in estimating the motion of cardiac ultrasound imaging. The OF computation is achieved by a method called LSF(least squares formulation). In sufficiently small region of interest in the image plane and small time interval, the OF vector can be formulated as a linear least square method .Preventing the imaging is ill-conditioned, we improve the LSF method by adding the concept of regularization. Since this improving, we can greatly reduce the appearance of ill OF vector. The experiments are consisted of three groups trials: the previous two trials are based on simulation imaging, and the last one is based on real cardiac ultrasound imaging. The motion vector is finally expressed in Vector diagram. This method has better accuracy than MSAD(minimum sum of absolute difference). Keywords-OF; motion estimation; LSF; cardiac ultrasound imaging; regularization I. INTRODUCTION Ultrasound has been widely used in medical field and supplies us a powerful tool in clinical diagnosis and treatment. The cardiac ultrasound application, which acts as an important branch of ultrasound field, attracts attention from more and more scholars. In this application, motion analysis of the cardiac structure and tissue helps doctors to catch the cardiac healthy condition of sufferers. There is a category of algorithm called OF(optical flow), which is raised for motion problem. OF is a classical algorithm in motion analysis and motion object detection. Hundreds of methods has been proposed to solve the OF computation. Most of the methods are classically based on the well-known Horn and Schunck model (1). The process of recovering OF embody a set of assumptions which, simply saying, may be violated by many factors. We have to consider lots of situation that violates the brightness constancy: the motion boundaries, shadows, or specular reflections. For the aim of reducing the possibility of assumption violation, it is necessary to denoise and smoothe the ultrasound imaging. The traditional technology based on optical flow computation costs many matrix operations and lots of time on iterating, but it's much more accurate in motion estimating comparing with the algorithms with none optical flow model, like MSAD and correlation. When recovering the OF vector field, we employ the LSF(least squares formulation) as the OF algorithm. We make an linear decomposition to the motion vector of each pixel and bring it to the OF constraints equation. Through minimizing the sum of luminous intensity variation in the ROI, we can get the motion vector. However, when we do the SVD(singular value decomposition), there exists another problem: the image is possibly to be ill-conditioned (2). If that case, the OF vector of the ill-conditioned area will be infinite large. Hence we have to regularize the matrix need to do SVD operation in the algorithm. Follow that step, we can avoid the motion vector ill-large. Visualization of motion vector is the ending step of this experiment. After getting the motion vector of each pixel, we will translate them into a vector diagram, which clearly express the motion pattern. In this paper, we take three groups of trials. The experiment starts with a simulation imaging trials. We compare the calculated OF vector field with the standard vector field, and get the error rate, which satisfies us. Next, we test the algorithm on a series of real continuous cardiac frames. To our joy the result is very good. |
