The separation of overlapping particles in three-dimensional images is an image processing task with many fields of application. However, commonly used image processing algorithms have difficulties to identify the single particles and their connections in certain structures. Here the authors present an alternative algorithm for part decomposition, which performs better on some structures than common algorithms. This algorithm is a special case of part decomposition, as it decomposes a structure at the necks into single particles. The necks are detected based on their characteristic negative Gaussian curvature. The algorithm itself consists of three steps: cutting at negative Gaussian curvature, region growing and intersecting plane minimisation. The authors tested the performance of the algorithm by comparison with two state-of-the-art algorithms for part decomposition, the watershed and a skeleton-based algorithm on strongly differing geometries, taken from natural snow samples. The two test algorithms are known for having difficulties to decompose certain structures. As the new algorithm uses a different characteristic to decompose the structure, the new algorithm is a good alternative to the existing algorithms. The new algorithm decomposes 72% of the reference structure correctly. This is a better performance than by the two other algorithms.