Thinning is for extracting unit-width skeletons from original objects. Such unit-width skeletons are useful in analyzing tree-structured objects, such bronchi or blood tubes. A tree-structured object could be segmented as a graph since the tails of different branches of the object may be too close and taken as cycles. One possible approach for extracting a tree structure from an original tree-oriented object is to extract a unit-width skeleton, then extract a tree structure from the unit-width skeleton. One major drawback of this approach is that the information of the thickness of each branch is vanished in the first step where the thickness of a branch is important in deciding which voxel should be reduced and which should not. This paper proposes an approach to obtain unit width tree structures from original tree-embedded objects directly through the thinning process.
To visualize, manipulate and analyze the geometrical structure of anatomical changes, it is often required to perform three-dimensional (3-D) interpolation of the interested organ shape from a series of cross-sectional images obtained from various imaging modalities, such as ultrasound, computed tomography (CT), magnetic resonance imaging (MRI), etc. In this paper, a novel wavelet-based interpolation scheme, which consists of four algorithms are proposed to 3-D image reconstruction. The multi-resolution characteristics of wavelet transform (WT) is completely used in this approach, which consists of two stages, boundary extraction and contour interpolation. More specifically, a wavelet-based radial search method is first designed to extract the boundary of the target object. Next, the global information of the extracted boundary is analyzed for interpolation using WT with various bases and scales. By using six performance measures to evaluate the effectiveness of the proposed scheme, experimental results show that the performance of all proposed algorithms is superior to traditional contour-based methods, linear interpolation and B-spline interpolation. The satisfactory outcome of the proposed scheme provides its capability for serving as an essential part of image processing system developed for medical applications.
Thinning on binary images is widely discussed in the past three decades. A binary image can be obtained by thresholding a gray-level image. For preventing possible information losses in the thresholding process, it may be natural to design thinning algorithms directly on the original gray-level images. This paper proposes a two-step template-based thinning algorithm on gray-level images. The first step of the algorithm is to extract 4-connected gray-level skeletons from gray-level objects. The second step is to extract 8-connected gray-level skeletons from the consequent result of the first step.
There are tow different kinds of elements in binary images: object pixels and background pixels. Many operations in image processing can be applied only to convert simple; pixels to background pixels. Some of these operations require such conversions must not change the connectivity structures of original images. Thinning is one of these operations. This paper established theoretical results. Such results are implemented into a computer package. The package is useful in designing new 2D thinning algorithms and is helpful in establishing 3D computerized thinning systems.
Thinning on two-tone images is widely discussed. Two-tone images can be obtained by thresholding gray-level images. One major advantage of using two-tone images is that a binary image can be transformed into a continuous image to which many properties of topology can be applied. However, its tradeoff is that the thresholding function may lose some information of the original gray-level images. Rosenfeld introduced digital topology in early 1970's and fuzzy digital topology in late 1970's by the stimulation of Zadeh's fussy theory in 1965. It may be natural to process thinning directly on gray-level images. This paper proposes a template-based thinning algorithm on gray-level images and generates gray-level skeletons.
A binary image contains object points and background points. Many operations on 2D and 3D images are required to preserve connectivity, that is, every object of the resulting image after the application of the operation preserves the same connectivity of the corresponding object in the original image. Normally, such operations can only delete `simple' object points. The simplicity of an object point can be determined by verifying its immediate neighborhood, i.e., a 3 X 3 neighborhood for the 2D case, or a 3 X 3 X 3 neighborhood for the 3D case, respectively. This verification for the 2D case is not difficult. However, it is not very easy for the 3D case since the number of different configurations of the 3D immediate neighborhood of a point is rather large. This paper studies some properties of this 3D problem and reduce it to a 2D problem.
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.
Thinning is a process which erodes an object layer by layer until only its skeleton is left. A thinning algorithm should preserve connectivity, i.e., any object and its skeleton should maintain the same connectivity structure. In this paper, we propose sufficient conditions so that any 3D 6-subiteration parallel thinning algorithm satisfying these conditions is guaranteed to preserve connectivity.
A thinning algorithm must `preserve topology,' but in the case of a parallel thinning algorithm it can be hard to prove that it does so. Ronse has given sufficient conditions which can be used to simplify such proofs in the 2D case. By Ronse's results, the fact that a parallel thinning algorithm is topology preserving can be verified by checking only a rather small number of configurations. This paper introduces Ronse-like sufficient conditions for 3D binary images.