On the base of the diameter of granule

the touching relationship of two objects in the image can be divided into three types: untouching

touching with different grain-size

touching with same grain-size. It also can be further divided into strong-touching

mid-touching and thin-touching by the size of touching part. The shape preserving segmentation of touching objects should be their original shape after segmentation

but watershed segmentation

geodesic reconstruction damage their shapes

and they are easily affected by many aspects. They also can't calculate the size of touching part. An alternative method is condition granulometry segmentation. After the erosion of image

the method doesn't dilation the marked area. It can segment different grain-size touching objects. For the same grain-size touching objects

using a special condition granulometry segmentation after erosion

the small grain-size(narrow piece) is the object touching part when reconstruction. In the end

the paper introduces the application to rock grain-size distribution and cement types of this algorithm.