Vázquez Carlos, Mitiche Amar, Laganière Robert
Advanced Video Systems, Communication Research Centre, Ottawa, Ontario, Canada.
IEEE Trans Pattern Anal Mach Intell. 2006 May;28(5):782-93. doi: 10.1109/TPAMI.2006.97.
The purpose of this study is to investigate a variational method for joint segmentation and parametric estimation of image motion by basis function representation of motion and level set evolution. The functional contains three terms. One term is of classic regularization to bias the solution toward a segmentation with smooth boundaries. A second term biases the solution toward a segmentation with boundaries which coincide with motion discontinuities, following a description of motion discontinuities by a function of the image spatio-temporal variations. The third term refers to region information and measures conformity of the parametric representation of the motion of each region of segmentation to the image spatio-temporal variations. The components of motion in each region of segmentation are represented as functions in a space generated by a set of basis functions. The coefficients of the motion components considered combinations of the basis functions are the parameters of representation. The necessary conditions for a minimum of the functional, which are derived taking into consideration the dependence of the motion parameters on segmentation, lead to an algorithm which condenses to concurrent curve evolution, implemented via level sets, and estimation of the parameters by least squares within each region of segmentation. The algorithm and its implementation are verified on synthetic and real images using a basis of cosine transforms.
本研究的目的是通过运动的基函数表示和水平集演化来研究一种用于图像运动联合分割和参数估计的变分方法。该泛函包含三项。一项是经典正则化项，使解偏向具有光滑边界的分割。第二项使解偏向边界与运动不连续点重合的分割，这是根据图像时空变化的函数对运动不连续点进行描述之后得到的。第三项涉及区域信息，并衡量分割的每个区域的运动参数表示与图像时空变化的一致性。分割的每个区域中的运动分量表示为一组基函数所生成空间中的函数。所考虑的作为基函数组合的运动分量的系数是表示的参数。考虑到运动参数对分割的依赖性而导出的泛函最小化的必要条件，导致一种算法，该算法可简化为通过水平集实现的并发曲线演化，并在分割的每个区域内通过最小二乘法估计参数。使用余弦变换基在合成图像和真实图像上对该算法及其实现进行了验证。
