3D Thinning Algorithm Research Articles

Three-dimensional characterizations of two-photon excitation fluorescence images of elastic fibers affected by cutaneous scar duration.

The type or duration of a scar determines the choice of therapy available. Traditional detection methods can easily cause secondary trauma, so there is an urgent need for a non-invasive, rapid diagnostic approach. A strategy for quantitative analysis of three-dimensional (3D) elastic fibers in human cutaneous scars was designed, which included 3D reconstruction, skeleton extraction, quantitative analysis, and random forest regression. Four reconstruction methods were used to reconstruct 3D two-photon excitation fluorescence images of elastic fibers for comparison. In the skeleton extraction stage, the 3D thinning algorithm was improved to prepare for accurate quantitative analysis, in which eight parameters comprising branches number (B-NUM), nodes number (N-NUM), averaged branch broken-line length (AB-BL), averaged linear branch length (AB-LL), averaged branch tortuosity (AB-T), branch direction consistency (B-DC), averaged branch volume (AB-V), and averaged branch sectional area (AB-SA) were presented. Six of them, except averaged branch tortuosity (AB-T) and branch direction consistency (B-DC), showed an explicit tendency to change with scar duration. In the random forests regression analysis, the six extracted parameters could be used to predict scar duration with R2=0.981 and RMSE=0.513. The parameters we extracted had a distinct relationship with scar duration, and random forests regression showed better performance in forecasting scar duration than unitary models.

Microcatheter Shaping for Intracranial Aneurysm Coiling Using Artificial Intelligence-Assisted Technique

Abstract INTRODUCTION A precise microcatheter shaping is critically necessary for the successful coiling of intracranial aneurysms. Currently, the development of artificial intelligence (AI)-based on technologies in medicine in advancing rapidly. The use of AI may have practical values in aiding the endovascular treatment of intracranial aneurysms. In this study, we tested the hypothesis that application of AI for analyzing parameters from three dimensional images, could warrant more accuracy and stability in microcatheter shaping during the treatment of intracranial aneurysms. METHODS Based on the 3-dimensional (3D) images of the digital subtraction angiography (DSA), we first segmented the vessels and the target aneurysms using a deep-learning-based method. Then the centerline of all vessels was extracted using a 3D thinning algorithm and the surface was calculated from the segmented binary maps. The simulated microcatheter path was then displayed in a 3D fashion together with the segmented vessels and aneurysms to assist the surgical planning and training process. After path simulation, the tip of the path was extracted and used to guide the steam-based shaping. The surgeons could then refer to the guidance during actual shaping. RESULTS A total of 22 patients with 22 aneurysms were treated with this technique. The average diameter of these aneurysms was 5.2 ± 2.9 mm. All of preplanned microcatheters matched vessel structures and aneurysm anatomy. Appropriate positioning was achieved in 15 (68.2%)patients without microguidewire assistance. In 5 cases (22.7%), microguidewire was used for microcatheter navigation and microcatheter reached the appropriate position. In 2 cases (9.1%) of ophthalmic aneurysm in the dorsal side of internal carotid artery, the microcatheter required modification for the initial shaping with reference to AI. During the operation, only 1 microcatheter (4.5%) required repositioning due to kick back during coil deployment. CONCLUSION AI-assisted microcatheter shaping techniques may be promising for faciliating easier and safer procedures in endovascular coiling of intracranial aneurysms.

Combined 3D thinning and greedy algorithm to approximate realistic particles with corrected mechanical properties

The shape of irregular particles has significant influence on micro- and macro-scopic behaviour of granular systems. This paper presents a combined 3D thinning and greedy set-covering algorithm to approximate realistic particles with a clump of overlapping spheres for discrete element method simulations. First, the particle medial surface (or surface skeleton), from which all candidate (maximal inscribed) spheres can be generated, is computed by the topological 3D thinning. Then, the clump generation procedure is converted into a greedy set-covering problem. To correct the mass distribution due to highly overlapped spheres inside the clump, linear programming is used to adjust the density of each component sphere, such that the aggregate properties mass, center of mass and inertia tensor are identical or close enough to the prototypical particle. In order to find the optimal approximation accuracy (volume coverage: ratio of clump’s volume to the original particle’s volume), particle flow of 3 different shapes in a rotating drum are conducted. It was observed that the dynamic angle of repose starts to converge for all particle shapes at 85% volume coverage (spheres per clump $$<30$$ ), which implies the possible optimal resolution to capture the mechanical behaviour of the system.

The Effectiveness of An Averaged Airway Model in Predicting the Airflow and Particle Transport Through the Airway.

Background: In this study, we proposed an averaged airway model design based on four healthy subjects and numerically evaluated its effectiveness for predicting the airflow and particle transport through an airway. Methods: Direct-averaged models of the conducting airways of four subjects were restored by averaging the three-dimensional (3D) skeletons of four healthy airways, which were calculated using an inverse 3D thinning algorithm. We simulated the airflow and particle transport in the individual and the averaged airway models using computational fluid dynamics. Results: The bifurcation geometry differs even among healthy subjects, but the averaged model retains the typical geometrical characteristics of the airways. The Reynolds number of the averaged model varied within the range found in the individual subject models, and the averaged model had similar inspiratory flow characteristics as the individual subject models. The deposition fractions at almost all individual lobes ranged within the variation observed in the subjects, however, the deposition fraction was higher in only one lobe. The deposition distribution at the main bifurcation point differed among the healthy subjects, but the characteristics of the averaged model fell within the variation observed in the individual subject models. On the contrary, the deposition fraction of the averaged model was higher than that of the average of the individual subject models and deviated from the range observed in the subject models. Conclusion: These results indicate that the direct-averaged model may be useful for predicting the individual airflow and particle transport on a macroscopic scale.

A 3D Skeletonization Algorithm for 3D Mesh Models Using a Partial Parallel 3D Thinning Algorithm and 3D Skeleton Correcting Algorithm

A three-dimensional (3D) skeletonization algorithm extracts the skeleton of a 3D model and provides it for many applications, such as 3D model classification and identification. There are three major skeletonization methodologies used in the literature, distance transform field-based methods, Voronoi diagram-based methods, and thinning-based methods. However, the existing algorithms cannot preserve the connectivity of the skeletons of the 3D mesh models. In this paper, we propose a 3D skeletonization algorithm for 3D mesh models using a partial parallel thinning algorithm and a 3D skeleton correcting algorithm. The proposed algorithm uses pre-defined removing and recovering templates. The partial parallel 3D thinning algorithm separates 62 symmetrical removing templates into two groups based on symmetry. It thins a model with the templates of each group in each thinning procedure. The 3D skeleton correcting algorithm uses six correcting templates to inspect the disconnected voxels in the skeleton and corrects them. The experimental results show several comparisons of skeletons extracted by different skeletonization algorithms. The proposed algorithm can extract the skeleton of each branch of a model and preserve the connectivity.

Automated generation of directed graphs from vascular segmentations

Automated feature extraction from medical images is an important task in imaging informatics. We describe a graph-based technique for automatically identifying vascular substructures within a vascular tree segmentation. We illustrate our technique using vascular segmentations from computed tomography pulmonary angiography images. The segmentations were acquired in a semi-automated fashion using existing segmentation tools. A 3D parallel thinning algorithm was used to generate the vascular skeleton and then graph-based techniques were used to transform the skeleton to a directed graph with bifurcations and endpoints as nodes in the graph. Machine-learning classifiers were used to automatically prune false vascular structures from the directed graph. Semantic labeling of portions of the graph with pulmonary anatomy (pulmonary trunk and left and right pulmonary arteries) was achieved with high accuracy (percent correct⩾0.97). Least-squares cubic splines of the centerline paths between nodes were computed and were used to extract morphological features of the vascular tree. The graphs were used to automatically obtain diameter measurements that had high correlation (r⩾0.77) with manual measurements made from the same arteries.

Automatic Correction of Ma and Sonka's Thinning Algorithm Using P-Simple Points

Ma and Sonka proposed a fully parallel 3D thinning algorithm which does not always preserve topology. We propose an algorithm based on P-simple points which automatically corrects Ma and Sonka's algorithm. As far as we know, our algorithm is the only fully parallel curve thinning algorithm which preserves topology.

Detection of the non-topology preservation of Ma and Sonka’s algorithm, by the use of P-simple points

In 1996, Ma and Sonka proposed a thinning algorithm which yields curve skeletons for 3D binary images [C. Ma, M. Sonka, A fully parallel 3D thinning algorithm and its applications, Comput. Vis. Image Underst. 64 (3) (1996) 420–433]. This algorithm is one of the most referred thinning algorithms in the context of digital topology: either by its use in medical applications or for comparisons with other thinning algorithms. In 2007, Wang and Basu [T. Wang, A. Basu, A note on ‘a fully parallel 3D thinning algorithm and its applications’, Pattern Recognit. Lett. 28 (4) (2007) 501–506] wrote a paper in which they claim that Ma and Sonka’s 3D thinning algorithm does not preserve topology. As they highlight in their paper, a counter-example was given in 2001, in Lohou’s thesis [C. Lohou, Contribution à l’analyse topologique des images: étude d’algorithmes de squelettisation pour images 2D et 3D selon une approche topologie digitale ou topologie discrète. Ph.D. thesis, University of Marne-la-Vallée, France, 2001]. In this paper, it is shown how P-simple points have guided the author towards a proof that Ma and Sonka’s algorithm does not always preserve topology. Moreover, the reasoning being very general, it could be reused for such a purpose, i.e., to simplify the proof on the non-topology preservation.

Detection of the non-topology preservation of Ma’s 3D surface-thinning algorithm, by the use of P-simple points

Recently, Wang and Basu [Wang, T., Basu, A., 2007. A note on ‘a fully parallel 3D thinning algorithm and its applications’. Pattern Recognition Lett. 28 (4), 501–506] have written a paper in which they claim that Ma and Sonka’s 3D thinning algorithm [Ma, C., Sonka, M., 1996. A fully parallel 3D thinning algorithm and its applications. Computer Vision and Image Understanding 64 (3), 420–433] does not preserve topology. As they highlight in their paper, a counterexample has been given in Lohou’s thesis [Lohou, C., 2001. Contribution à l’analyse topologique des images: étude d’algorithmes de squelettisation pour images 2D et 3D selon une approche topologie digitale ou topologie discrète. Ph.D. thesis, Univ. de Marne-la-Vallée, France]. In fact, the previous Ma’s algorithm [Ma, C., 1995. A 3D fully parallel thinning algorithm for generating medial faces. Pattern Recognition Lett. 16, 83–87] does not preserve topology. The goal of this paper is to show how P-simple points have guided us towards a proof that Ma’s algorithm does not always preserve topology.

Implementation of a 3D thinning algorithm

ITK currently comes with a 2D binary thinning (skeletonisation) method, but does not support 3D or higher. This paper documents a new itkBinaryThinningImageFilter3D and recommends to rename the current filter as itkBinaryThinningImageFilter2D.The 3D method suggested here is a direct implementation of the work of Lee et al. [2] who have demonstrated that their algorithm can find all deletable surface points at every iteration and is thus very fast. The code was tested on six clinical datasets.

Solid Breast Masses: Neural Network Analysis of Vascular Features at Three-dimensional Power Doppler US for Benign or Malignant Classification

To retrospectively evaluate the accuracy of neural network analysis of tumor vascular features at three-dimensional (3D) power Doppler ultrasonography (US) for classification of breast tumors as benign or malignant, with histologic findings as the reference standard. This study was approved by the local ethics committee; informed consent was waived. Three-dimensional power Doppler US images of 221 solid breast masses (110 benign, 111 malignant) were obtained in 221 women (mean age, 46 years; range, 25-71 years). After narrowing down vessels to skeletons with a 3D thinning algorithm, six vascular feature values--vessel-to-volume ratio, number of vascular trees, total vessel length, longest path length, number of bifurcations, and vessel diameter-were computed. A neural network was used to classify tumors by using these features. Independent-samples t test and receiver operating characteristic (ROC) curve analysis were used. Mean values of vessel-to-volume ratio, number of vascular trees, total vessel length, longest path length, number of bifurcations, and vessel diameter were 0.0089 +/- 0.0073 (standard deviation), 26.41 +/- 14.73, 23.02 cm +/- 19.53, 8.44 cm +/- 10.38, 36.31 +/- 37.06, and 0.088 cm +/- 0.021 in malignant tumors, respectively, and 0.0028 +/- 0.0021, 9.69 +/- 6.75, 5.17 cm +/- 4.78, 1.68 cm +/- 1.79, 6.05 +/- 7.55, and 0.064 cm +/- 0.028 in benign tumors, respectively (P < .001 for all six features). Area under ROC curve (A(z)) values of the six features were 0.84, 0.87, 0.87, 0.82, 0.84, and 0.75, respectively. Accuracy, sensitivity, specificity, and positive and negative predictive values were 85% (187 of 221), 83% (96 of 115), 86% (91 of 106), 86% (96 of 111), and 83% (91 of 110), respectively, with A(z) of 0.92 based on all six feature values. Three-dimensional power Doppler US images and neural network analysis of features can aid in classification of breast tumors as benign or malignant.

A note on ‘A fully parallel 3D thinning algorithm and its applications’

A 3D thinning algorithm erodes a 3D binary image layer by layer to extract the skeletons. This paper presents a correction to Ma and Sonka’s thinning algorithm, ‘A fully parallel 3D thinning algorithm and its applications’, which fails to preserve connectivity of 3D objects. We start with Ma and Sonka’s algorithm and examine its verification of connectivity preservation. Our analysis leads to a group of different deleting templates, which can preserve connectivity of 3D objects.

Three-Dimensional Pore Structure of Chromatographic Adsorbents from Electron Tomography

The pore structure of chromatographic adsorbents directly influences macromolecular partitioning and transport in chromatography. Quantitative structural characterization of chromatographic media has generally been performed in terms of the mean pore size or, at best, the pore size distribution (PSD), but more detailed information on, e.g., connectivity has been lacking. We have applied electron tomography, a 3D TEM technique that views a sample from multiple perspectives and allows reconstruction of the volumetric structure, to capture the internal details of microporous chromatographic media with nanometer-scale resolution. Visualization of reconstructions of three adsorbents, Toyopearl SP-650 C, SP-550 C, and CM Sepharose FF, provides thorough and direct information on the geometry and the interconnectivity of the pore network. The structures are qualitatively consistent with in situ AFM images, and quantitative data for the porosities and PSDs from the analysis of tomographic data agree reasonably well with inverse size-exclusion chromatography results. For a more straightforward representation of the networking and size features of the disordered pore space, a 3D thinning algorithm was used to derive pore skeletons and consequently quantitative data on distributions of local path lengths, widths, tortuosities, and connectivities. Such enriched structural information can be instrumental in more discriminate structural evaluation and construction of engineered pore models for the study of solute intraparticle transport.

A 3D 6-subiteration curve thinning algorithm based on P-simple points

In a recent study C. Lohou, G. Bertrand [A new 3D 12-subiteration thinning algorithm based on P-simple points, in: International Workshop on Combinatorial Image Analysis, IWCIA 2001, Philadelphia, PA, USA, ENTCS, vol. 46, 2001, pp. 39–58; A new 3D 6-subiteration thinning algorithm based on P-simple points, in: International Conference on Discrete Geometry for Computer Imagery, DGCI’2002, Bordeaux, France, ENTCS, vol. 2301, Springer, Berlin, 2002, pp. 102–113; A 3D 12-subiteration thinning algorithm based on P-simple points, Discrete Appl. Math. 139(1–3) (2004) 171–195.], we proposed a new methodology to build thinning algorithms based on the deletion of P-simple points. This methodology may permit to conceive a thinning algorithm A ′ from an existent thinning algorithm A, such that A ′ deletes at least all the points removed by A, while preserving the same end points (in particular, we have already proposed a 12-subiteration thinning algorithm C. Lohou, G. Bertrand [International Workshop on Combinatorial Image Analysis, IWCIA 2001, Philadelphia, PA, USA, ENTCS, vol. 46, 2001, pp. 39–58; A 3D 12-subiteration thinning algorithm based on P-simple points, Discrete Appl. Math. 139(1–3) (2004) 171–195.]). In this paper, by applying this methodology, we propose a 6-subiteration curve thinning algorithm which deletes at least all the points removed by two 6-subiteration curve thinning algorithms: either the one proposed by Palágyi and Kuba [A 3D 6-subiteration thinning algorithm for extracting medial lines, Pattern Recogn. Lett. 19(7) (1998) 613–627.], or the one proposed by Gong and Bertrand [A simple parallel 3D thinning algorithm, in: International Conference on Pattern Recognition, Atlantic City, NJ, USA, 1990, pp. 188–190.].

Three-dimensional segmentation and skeletonization to build an airway tree data structure for small animals

Quantitative analysis of intrathoracic airway tree geometry is important for objective evaluation of bronchial tree structure and function. Currently, there is more human data than small animal data on airway morphometry. In this study, we implemented a semi-automatic approach to quantitatively describe airway tree geometry by using high-resolution computed tomography (CT) images to build a tree data structure for small animals such as rats and mice. Silicon lung casts of the excised lungs from a canine and a mouse were used for micro-CT imaging of the airway trees. The programming language IDL was used to implement a 3D region-growing threshold algorithm for segmenting out the airway lung volume from the CT data. Subsequently, a fully-parallel 3D thinning algorithm was implemented in order to complete the skeletonization of the segmented airways. A tree data structure was then created and saved by parsing through the skeletonized volume using the Python programming language. Pertinent information such as the length of all airway segments was stored in the data structure. This approach was shown to be accurate and efficient for up to six generations for the canine lung cast and ten generations for the mouse lung cast.

A 3D 12-subiteration thinning algorithm based on P-simple points

In this paper, we propose a new methodology to conceive a thinning scheme based on the parallel deletion of P-simple points. This scheme needs neither a preliminary labelling nor an extended neighborhood, in the opposite of the already proposed thinning algorithms based on P-simple points. Moreover, from an existent thinning algorithm A, we construct another thinning algorithm A′, such that A′ deletes at least all the points removed by A, while preserving the same end points. In fact, we propose a 12-subiteration thinning algorithm which deletes at least the points removed by the one proposed by Palágyi and Kuba (Graphical Models Image Process. 61 (1999) 199).

Connectivity and topology of a phase-separating bicontinuous structure in a polymer mixture: Direct measurements of coordination number, inter-junction distances and Euler characteristic

A new set of topological parameters describing connectivity of a phase-separated bicontinuous structure of a polymer mixture in the late stage of spinodal decomposition has been directly measured by use of laser scanning confocal microscopy. A 3D thinning algorithm was used to transform one of the phase-separated domains into a skeletal network that locates at about the center of the domain. Number of channels intersecting at a junction, Nj, and distance between the adjacent junctions, Dj, were obtained from the resulting skeletal network. It was found that the phase-separated domain of the polymer mixture possesses, for the most part, 3 branches at each junction. The Euler characteristic, describing topology of the network, was found to be between ∼−2 to −4, topologically equivalent to a sphere with ∼2 to 3 handles. Time-evolution of the histograms of the coordination number, H(Nj), and distance, H(Dj), clearly demonstrates that the bicontinuous structure grows with self-similarity in topological sense.

Automatic 3D vascular tree construction in CT angiography

This study presents an automatic method for 3D reconstruction of vascular trees using computed-tomography angiographic (CTA) images. The program starts with the CTA slices, performs a sequential procedure of 3D image formation, preprocessing, segmentation, thinning, skeleton pruning and tree construction. It ends with vascular trees along with quantitative data about the trees such as values of diameter, length and bifurcation angles. All the involved algorithms are presented with the emphasis given to the skeleton pruning and tree construction algorithms. The skeletons obtained using a 3D thinning algorithm may contain cycles, spurs, isolated sticks, and non-unit-width parts, which hinder tree construction. As a solution to this problem, a skeleton pruning and tree construction algorithm is proposed. At each stage of the automatic procedure, 3D rendering is provided for visual inspection of the computed results. In the final output, the constructed vascular trees are visualized by rendering the 3D trees and the 3D binary image together in a transparent display mode. The program is carried out in a fully automatic fashion, with a few default settings. Occasionally, user intervention is needed at the 3D segmentation stage to impose an appropriate threshold when the automatic 3D segmentation is obviously sub-optimal for vessel delineation. Experimental demonstrations on both coronary artery phantom and a cast of coronary artery tree of a swine animal model are provided.

A topology-preserving parallel 3D thinning algorithm for extracting the curve skeleton

We introduce a new topology-preserving 3D thinning procedure for deriving the curve voxel skeleton from 3D binary digital images. Based on a rigorously defined classification procedure, the algorithm consists of sequential thinning iterations each characterized by six parallel directional sub-iterations followed by a set of sequential sub-iterations. The algorithm is shown to produce concise and geometrically accurate 3D curve skeletons. The thinning algorithm is also insensitive to object rotation and only moderately sensitive to noise. Although this thinning procedure is valid for curve skeleton extraction of general elongated objects, in this paper, we specifically discuss its application to the orientation modeling of trabecular biological tissues.

Three-dimensional topology preserving reduction on the 4-subfields

This paper discusses thinning on 3D binary images with the 4-subfield approach. Although a thinning algorithm concerns binary images, the algorithm itself can be represented as a set of three-color reduction templates. A thinning algorithm is topology preserving if the set of all three-color templates is topology preserving. Sufficient and necessary conditions of time complexity O(n) were proposed for verifying the topological soundness of a 3D 4-subfield thinning algorithm of n three-color templates. Theories and techniques for computerizing such conditions were discussed. Two 4-subfield thinning algorithms on 3D images, one for generating medial curves, and the other one for generating medial surfaces, are proposed and proved to preserve topology by our sufficient and necessary conditions.