Important properties of 3D simplicity

There are two different kinds of elements in binary images: object points and background points. A simple point is an object point whose conversion to a background point does not change the connectivity of the original image. Many operations in image processing can be applied only to convert simple points to background points. Finding an efficient method for determining the simplicity of an object point is an interesting research topic. Although 2D simplicity has been extensively studied recently, more work needs to be done for 3D simplicity. This paper studies important properties of 3D simplicity which may be useful in certain operations of image processing, for example, thinning.