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Marching Cubes and Histogram Pyramids for 3D Medical Visualization

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Marching Cubes and Histogram Pyramids for 3D Medical Visualization Journal of Imaging Article Marching Cubes and Histogram Pyramids for 3D Medical Visualization Porawat Visutsak Department of Computer and Information Science, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand; [email protected]; Tel.: +66-2555-2000 (ext. 4225) Received: 1 July 2020; Accepted: 31 August 2020; Published: 3 September 2020 Abstract: This paper aims to implement histogram pyramids with marching cubes method for 3D medical volumetric rendering. The histogram pyramids are used for feature extraction by segmenting the image into the hierarchical order like the pyramid shape. The histogram pyramids can decrease the number of sparse matrixes that will occur during voxel manipulation. The important feature of the histogram pyramids is the direction of segments in the image. Then this feature will be used for connecting pixels (2D) to form up voxel (3D) during marching cubes implementation. The proposed method is fast and easy to implement and it also produces a smooth result (compared to the traditional marching cubes technique). The experimental results show the time consuming for generating 3D model can be reduced by 15.59% in average. The paper also shows the comparison between the surface rendering using the traditional marching cubes and the marching cubes with histogram pyramids. Therefore, for the volumetric rendering such as 3D medical models and terrains where a large number of lookups in 3D grids are performed, this method is a particularly good choice for generating the smooth surface of 3D object. Keywords: marching cubes; histogram pyramids; volumetric rendering; 3D medical model; smooth voxel; isosurface 1. Introduction 3D visualization methods of human bone and organs were applied to diagnosis as long as 100 years ago [1]. Normally, 3D medical imaging system aims to provide both quantitative and qualitative information for diagnosis. 3D visualization system can be divided into 4 operations: (1) preprocessing that deals with the volume of interest and features extraction; (2) visualization processes generate 3D object from 2D images; (3) manipulation explains the geometry of object that can be distorted and deformed; (4) analysis that deals with methods of quantify 3D object [2]. For medical volumetric rendering where 2D binary images (CT-volume) are feed to construct 3D object, collision detection algorithm is used to manipulate the intersecting fragments and generate triangulated mesh models (see Figure1a). The doctor can take this advantage of training by observing the demonstration of context of 3D manipulation of bone fragments and the resulting CT images [3]. More works of 3D visualization such as texture mapping and semi-automatic image segmentation. Texture mapping technique constructs 3D object by interpreting the spatial relationships of 2D binary images and generates 3D visualization of perspective-mapped from each image layer [4]. Whereas, semi-automatic image segmentation allows the doctor to make the segmentation of subject by the area of interest [5]. Therefore, the major drawback of these methods is the computational cost of real time resampling for making texture in 3D object reconstruction process [4], and infeasibility for each individual segmentation [5] (see Figure1b,c). The alternative choice for 3D volumetric rendering is marching cubes. The marching cubes method keeps the coordinates conveyed by traversing the outline of 2D binary shape and marches them to construct 3D object [6–10]. The algorithm is based J. Imaging 2020, 6, 88; doi:10.3390/jimaging6090088 www.mdpi.com/journal/jimaging J. Imaging 2020, 6, 88x FOR PEER REVIEW 2 of 12 J. Imaging 2020, 6, x FOR PEER REVIEW 2 of 12 on the configuration of 15 fundamental cubes (see Section 2). Figure 2 shows 3D human head model on the configurationconfiguration ofof 1515 fundamentalfundamental cubescubes (see(see SectionSection2 2).). FigureFigure2 2shows shows 3D 3D human human head head model model constructed by marching cubes method; the method used 150 slides of 2D image as input source. constructedconstructed byby marchingmarching cubescubes method;method; thethe methodmethod usedused 150150 slidesslides ofof 2D2D imageimage asas inputinput source.source. (a) (b) (a) (b) (c) (c) Figure 1. (a) Bone fracture displays in 3D visualization software, the Sobel-filter is used for detecting Figure 1.1. (a) Bone fracture displays in 3D visualization software,software, thethe Sobel-filterSobel-filter isis usedused forfor detectingdetecting the outline of bone [11]; (b) CT image slides and (c) 3D visualization [4]. thethe outlineoutline ofof bonebone [[11];11]; ((bb)) CTCT imageimage slidesslides andand ((cc)) 3D3D visualizationvisualization [[4].4]. Figure 2. 3D human head model, constructed by marching cubes method (the original source file file of Figure 2. 3D human head model, constructed by marching cubes method (the original source file of this figure figure is [[12]).12]). this figure is [12]). It seems like the marching cubes can reduce the computational time used for resampling in 3D It seems like the marching cubes can reduce the computational time used for resampling in 3D reconstruction,It seems like but the the marching problem cubes still remains can reduce in observing the computational the qualitative time used information for resampling of 3D surface in 3D reconstruction, but the problem still remains in observing the qualitative information of 3D surface constructedreconstruction, using but marching the problem cubes. still One remains major in problem observing of marching the qualitative cubes is information the unused of voxels 3D surface which constructed using marching cubes. One major problem of marching cubes is the unused voxels which canconstructed be generated using during marching parsing cubes. the One coordinates major problem and the of intensity marching values cubes of is 2Dthe images,unused thesevoxels unused which can be generated during parsing the coordinates and the intensity values of 2D images, these unused voxelscan be ageneratedffect for the during smoothness parsing of the 3D coordinates surface (the an detaild the ofintensity the surface values smoothness of 2D images, will these be explained unused voxels affect for the smoothness of 3D surface (the detail of the surface smoothness will be explained invoxels Sections affect4 andfor the6). smoothness To overcome of this 3D surface drawback, (the this detail paper of the introduces surface smoothness histogram will pyramids be explained with in Sections 4 and 6). To overcome this drawback, this paper introduces histogram pyramids with marchingin Sections cubes 4 and method 6). To forovercome 3D medical this volumetricdrawback, rendering.this paper Theintroduces histogram histogram pyramids pyramids organize with the marching cubes method for 3D medical volumetric rendering. The histogram pyramids organize the imagemarching entries cubes to formmethod the for voxel 3D related medical to volumetric the index values, rendering. the traversal The histogram of histogram pyramids pyramids organize is used the image entries to form the voxel related to the index values, the traversal of histogram pyramids is toimage construct entries the to point form listthe that voxel will related be later to usedthe index for generating values, the the traversal voxel. Theof histogram organization pyramids of paper is used to construct the point list that will be later used for generating the voxel. The organization of consistsused to ofconstruct (1) Introduction, the point (2)list The that brief will conceptbe later of used marching for generating cubes method, the voxel. (3) Reading The organization the intensity of paper consists of (1) Introduction, (2) The brief concept of marching cubes method, (3) Reading the paper consists of (1) Introduction, (2) The brief concept of marching cubes method, (3) Reading the J. Imaging 2020, 6, 88 3 of 12 J. Imaging 2020, 6, x FOR PEER REVIEW 3 of 12 valueintensity of CT value images of CT for 3Dimages rendering, for 3D (4) rendering, Histogram (4) pyramids, Histogram (5) Implementation,pyramids, (5) Implementation, (6) Results, and (6) (7) ConclusionResults, and and (7) Conclusion future works. and future works. 2. Marching Cubes Original marching cubes cubes algorithm algorithm was was developed developed by by [6], [6 ],later later works works applied applied this this algorithm algorithm for for3D rendering 3D rendering using using 2D medical 2D medical images images(CT: Comp (CT:uted Computed Tomography Tomography Scan, MRI: Scan, Magnetic MRI: Resonance Magnetic ResonanceImaging, and Imaging, SPECT: and Single-Photon SPECT: Single-Photon Emission Computed Emission ComputedTomography) Tomography) sequence as sequence an input. as The an input.marching The cubes marching algorithm cubes will algorithm be explained will be later explained in this later section. in this More section. works More of volume works ofrendering volume renderingtechniques techniques such as [7] such used as [sampled7] used sampled scalar functi scalarons functions for displaying for displaying 3D surfaces, 3D surfaces, [8] presented [8] presented the theextended extended version version of ofvolume volume rendering rendering that that used toto handle handle images images with with mixtures mixtures properties properties (color (color and texture).and texture). To deal To withdeal thewith boundary the boundary value value problems problems which which are the are main the task main for
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