目的 针对基于矢量场的活动轮廓模型，如经典的梯度矢量流（GVF）模型、矢量场卷积（VFC）模型等，在提取凹形物体时矢量场常出现平衡点，不能较好地收敛到凹陷区域、尤其是深而窄的凹形及复杂凹陷区域的问题。提出一种融合凹点检测与仿射变换的活动轮廓模型。方法 首先利用活动轮廓模型进行曲线演化，得到演化后轮廓曲线上各点的坐标并求出各点的法线方向；然后基于凹点检测的方法，判断各点的凹凸性，利用梯度判断法，检测出未收敛到目标边界的凹点；其次对各凹点进行法向方向的仿射变换。在接近且不越过目标边界的情况下求出可变换的最大距离，变换后的点穿越了平衡点区域，让变换后的点代替原来的点形成新的轮廓曲线；最后为保证提取边界的精确性，将变换后的轮廓曲线再次演化并最终收敛到目标边界。结果 通过对具有凹陷区域的合成图像进行分割，计算提出模型分割结果的平均Jaccard相似系数（JS）值为95.51%，相比目前先进的GVF模型，VFC模型和自适应扩散流（ADF）模型分别提高了15.08%，12.09%和10.70%，整体效果上优于几种先进的模型。然后又对单/多目标真实图像及含噪的图像进行分割，证实提出模型分割性能的鲁棒性。结论 提出的模型有效地避免了凹形区域内的平衡点问题，可以对深凹形及复杂凹形图像进行有效分割，并且提高了分割精度。此外，该模型能融合到任何基于矢量场的活动轮廓模型中，具有广泛的普适性。

Objective The active contour model is a widely used method in image segmentation. The basic idea of the traditional parametric active contour model is to define an initial curve composed of control points, and make the curve as close to the target as possible, by defining the energy function and finding the minimum value to obtain the edge contour of the target object, because of its sensitivity to initialization, small capture range and can not converge to the concave area and other shortcomings, so that the initial contour must be set close to the edge of the target object in order to get a better segmentation results, or can not effectively extract the target edge contour or extract the results are not accurate. Some scholars have made improvements on this basis and proposed various active contour models based on vector fields, such as classical gradient vector flow (GVF), vector field convolution (VFC), adaptive diffusion flow (ADF) model and other models, these vector-based active contour models use the new external force field instead of the original Gaussian force field. Although the shortcomings of the traditional parametric active contour model are solved, the initial contour is insensitive, and the capturing range is extended, for some simple images with concave regions, the boundary can be extracted accurately, but there is still a problem of premature convergence for image of containing complex concave. For the vector contour model based on the vector field, the vector field often appears at the equilibrium point when extracting the concave object, resulting in premature convergence, it can not be better convergence to the depression area, especially deep and narrow concave and complex depression area. An active contour model integrating concave point detection and affine transformation is proposed to solve the above problems. Method Because VFC model is not sensitive to initialization, can enter a part of the concave area, and the calculation is simple, so this paper chooses the VFC model based on the fusion concave point detection and affine transformation method. First, the VFC active contour model based on vector field is used to simulate the curve. The coordinates of the points on the contour curve are obtained, and the normal direction of each point is obtained. And then use the method of concave point detection to judge the concavity and convexity of each point, concave points are extracted separately, the concave point that does not converge to the target boundary is detected by the gradient method; Second, the affine transformation of these concave points is extended to the normal direction, and the maximum distance can be obtained without approaching and not crossing the target boundary, a new contour curve is formed by replacing the original points with the transformed points, and the transformed points cross the area of equilibrium point, have the force to continue converging to the concave area; Finally, in order to ensure the accuracy of the extraction boundary, the new contour curve will be transformed once again, and finally converge to the target boundary, the complete object is extracted. Result The GVF model, VFC model, ADF model and the proposed model were tested and compared respectively in the data sets of the composite images with concave regions, single/multi-target real images and noise images. By dividing the synthetic image with the concave area, it shows that the proposed model is superior to the concave area segmentation, and can accurately enter the concave area and the calculation is simple, on the basis of this, the average JS value of the model segmentation is 95.51%. Compared with the current advanced active contour model based on vector field:GVF model, VFC model and ADF model, the similarity of model segmentation results is improved 15.08%, 12.09% and 10.70% respectively, the overall effect is superior to the mention of these advanced models, which not only solves the problem of edge contour extraction of target objects in concave area, but also improves the accuracy of segmentation. Then, segmentation of single/multi-target images and noise images, the experimental results show that the proposed model can improve the robustness of the segmentation performance on the basis of maintaining the good segmentation effect of the original model. Conclusion The model proposed by the fusion concave points detection and affine transformation effectively avoids the problem of the equilibrium point which is often found in the concave area of the active contour model based on the vector field. It not only achieves the effective segmentation of the deep concave and the complex concave image, but also improves the segmentation accuracy so that the extracted edge contour is closer to the real boundary of the target object. In addition, although this paper is a fusion of concave point detection and affine transform based on the VFC model, but the fusion of concave point detection and affine transform in active contour model is introduced to solve the equilibrium problem can be applied to any vector field based on active contour model, and has wide universality. This paper mainly solves the problem that the active contour model based on vector field appears the equilibrium point in the process of evolution of concave area, the problem of premature convergence leads to the in correctly edge contour, and there is not too much consideration of multi-objective image segmentation, background and noise effects, although the proposed model to maintain the excellent segmentation characteristics of original model to solve these problems, but also need a lot of experiments to test, verify. So this problem can be used as the next step to improve the direction of the model, continue in-depth study.