• Journal of Biomedical Engineering Research
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• v.26 no.2
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• pp.73-86
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• 2005

We need to flatten the brain cortex to smooth surface, sphere, or 2D plane in order to view the buried sulci. The rendered 3D surface of the segmented white matter and gray matter does not have the topology of a sphere due to the partial volume effect and segmentation error. A surface without correct topology may lead to incorrect interpretation of local structural relationships and prevent cortical unfolding. Although some algorithms try to correct topology, they require heavy computation and fail to follow the deep and narrow sulci. This paper proposes a method that corrects topology of the rendered surface fast, accurately, and automatically. The proposed method removes fractions beside the main surface, fills cavities in the inside of the main surface, and removes handles in the surface. The proposed method to remove handles has three-step approach. Step 1 performs smoothing operation on the rendered surface. In Step 2, vertices of sphere are gradually deformed to the smoothed surfaces and finally to the boundary of the segmented white matter and gray matter. The Step 2 uses multi-resolutional approach to prevent the deep sulci from geometrical intersection. In Step 3, 3D binary image is constructed from the deformed sphere of Step 2 and 3D surface is regenerated from the 3D binary image to remove intersection that may happen. The experimental results show that the topology is corrected while principle sulci and gyri are preserved and the computation amount is acceptable.

• Journal of the Korean Society for Precision Engineering
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• v.16 no.9
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• pp.172-178
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• 1999

3D linear and circular interpolations are a basic part for the machining of complex shapes. Until now, because of the absence of appropriate algorithms for the generation of 3D lines and circles, a full accomplishment for available machine tool resolution is difficult. this paper presents new algorithms for 3D linear and circular interpolation in the reference pulse technique. In 3D space, the line or circle is not expressed as an implicit function, it is only defined as the intersection of two surfaces. A 3D line is defined as the intersection of two planes, and a 3D circle is defined as the intersection of a plane and the surface of a sphere. Based on these concepts, interpolation algorithms are designed to follow intersection curves in 3D space, and a real-time 3D linear and circular interpolator was developed in software using a PC. The algorithm implemented in a PC showed promising results in interpolation error and speed performance. It is expected that it can be applied to the next generation computerized numerical control systems for the machining of 3D lines, circles and some other complex shapes.

• International Journal of Contents
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• v.12 no.2
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• pp.42-48
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• 2016

We present efficient algorithms for computing centroid directions for each of the three types of monotonicity in a polyhedron: strong, weak, and directional monotonicity, which can be used for optimizing directions in many 3D manufacturing processes. Strongly- and directionally-monotone directions are the poles of great circles separating a set of spherical polygons on the unit sphere, the centroids of which are shown to be obtained by applying the previous result for determining the maximum intersection of the set of their dual spherical polygons. Especially in this paper, we focus on developing an efficient method for approximating the weakly-monotone centroid, which is the pole of one of the great circles intersecting a set of spherical polygons on the unit sphere. The original problem is approximately reduced into computing the intersection of great bands for avoiding complicated computational complexity of non-convex objects on the unit sphere, which can be realized with practical linear-time operations.

• Journal of Korea Multimedia Society
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• v.7 no.12
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• pp.1700-1707
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• 2004

Nowaday, market size of digital image in world around is looks to rapidly growth. For this, Texture mapping has traditionally been used to add realism to computer graphics images. Therefore to make our image realistic, we need to give the various kind of objects material parameter and environment lighting. To present the completed marble we use passing back algorithm and combination with channel of a material. In experimental result of this paper that application by passing back algorithm and varying the parameter such as scale, period, distortion, octaves of noise make showing the superiority of optimized rendering of spheres and perfect another marble effects.