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. 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