目的 针对图像目标边界不连续或具有模糊性导致的目标周长无法精确估算这一问题，结合边界跟踪，提出一种基于灰度级信息的目标边界精确周长估算方法。方法 该方法利用目标边界的灰度级信息，同时结合边界跟踪得到的内外边界来估计目标图像的边界周长，从而提高边界周长估计的精确性和鲁棒性。为了获得目标物体真实周长，实验采用人工合成图像。结果 实验应用所提方法和3种传统周长估算方法分别计算合成目标对象的周长，并与真实周长比较。为了验证所提方法的有效性和鲁棒性，实验中对目标对象的边界进行不同程度的加厚模糊化；并在边界加入噪声，使边界不连续。当边界变得复杂时，本文所提方法的优势得到极大体现。结论 实验结果表明，在边界模糊和边界不连续的情况下，本文所提的算法具有更好的适应性和稳定性。

Objective The perimeter of a target boundary in a 2D image is an essential object feature in image analysis. However, this feature is usually inaccurately estimated because of discontinuous or blurred target boundaries. Accordingly, this study proposes an improved method of perimeter estimation. This method is based on gray-level information and combined with boundary tracking. Method Different from the traditional methods that generally use binary information to calculate the perimeter, the proposed method utilizes gray-level information in digital images to obtain substantial information on a target boundary. The concepts of pixel coverage, internal boundary, and external boundary are introduced. The slope at each configuration on the internal and external boundaries is computed, and the perimeters of the internal and external boundaries are estimated based on the arc length integration formula. The perimeter of the target object boundary is obtained by combining the perimeter information on the internal and external boundaries. Result The perimeters of the target object boundaries are estimated using the proposed method and three classical methods. Synthetic images are used to obtain the exact perimeters of the target objects. The results are compared with the ground truth perimeters of the target objects in synthetic images. In the first two experiments, synthetic images with continuous and blurred boundaries are tested. The performance of the proposed method is similar to that of the classical methods but is better than that of the original gray-level method. In the third experiment, synthetic images with discontinuous and blurred boundaries are tested. In this case, the two classical geometrical methods are not applicable, whereas the proposed method remains to have satisfactory performance. The advantage of the proposed method is more obvious when the boundary of the target is complex. Conclusion Compared with the classical methods, the proposed method has better adaptability and stability for target objects with blurred or discontinuous boundaries.