The minimal geodesic models based on the Eikonal equations are capable of finding suitable solutions in various image segmentation scenarios. Existing geodesic-based segmentation approaches usually exploit image features in conjunction with geometric regularization terms, such as Euclidean curve length or curvature-penalized length, for computing geodesic curves. In this paper, we take into account a more complicated problem: finding curvature-penalized geodesic paths with a convexity shape prior. We establish new geodesic models relying on the strategy of orientation-lifting, by which a planar curve can be mapped to an high-dimensional orientation-dependent space. The convexity shape prior serves as a constraint for the construction of local geodesic metrics encoding a particular curvature constraint. Then the geodesic distances and the corresponding closed geodesic paths in the orientation-lifted space can be efficiently computed through state-of-the-art Hamiltonian fast marching method. In addition, we apply the proposed geodesic models to the active contours, leading to efficient interactive image segmentation algorithms that preserve the advantages of convexity shape prior and curvature penalization.
翻译:以 Eikonal 等式为基础的最低大地学模型能够找到各种图像分割情景的合适解决方案。 现有的大地学分化方法通常利用图像特征与几何正规化条件相结合, 如 Euclidean 曲线长度或曲线- 弯曲- 弯曲长度, 用于计算大地学曲线。 在本文中, 我们考虑到一个更为复杂的问题: 找到具有前相近形状的曲线- 断面化大地学路径; 我们根据定向提升战略建立新的大地学模型, 由此绘制平面曲线到一个高度方向依赖的空间。 之前的二次曲线形状作为构建本地大地学测量测量测量参数的制约, 将特定的曲度限制编码。 然后, 方向调整后的空间的大地学距离和相应的封闭的大地学路径可以通过状态- 艺术 汉密尔顿 快速行进法 高效地计算。 此外, 我们将拟议的大地学模型应用到活跃的轮廓上, 导致高效的交互式交互图像分解算法, 从而维护着曲线前的优势 。