page_title: 3D reconstruction
section_title: 3D Reconstruction of medical images
hierarchical_section_title: 3D reconstruction / Passive methods / Binocular stereo vision / 3D Reconstruction of medical images
caption_attribution_description: English: Solid geometry with volume rendering Image courtesy of Patrick Chris Fragile Ph.D., UC Santa Barbara
context_page_description: In computer vision and computer graphics, 3D reconstruction is the process of capturing the shape and appearance of real objects.
  This process can be accomplished either by active or passive methods. If the model is allowed to change its shape in time, this is referred to as non-rigid or spatio-temporal reconstruction.
context_section_description: Clinical routine of diagnosis, patient follow-up, computer assisted surgery, surgical planning etc. are facilitated by accurate 3D models of the desired part of human anatomy. Main motivation behind 3D reconstruction includes
  Improved accuracy due to multi view aggregation.
  Detailed surface estimates.
  Can be used to plan, simulate, guide, or otherwise assist a surgeon in performing a medical procedure.
  The precise position and orientation of the patient's anatomy can be determined.
  Helps in a number of clinical areas, such as radiotherapy planning and treatment verification, spinal surgery, hip replacement, neurointerventions and aortic stenting.
  Applications:
  3D reconstruction has applications in many fields. They are: 
  Pavement engineering
  Medicine
  Free-viewpoint video reconstruction
  Robotic mapping
  City planning
  Tomographic reconstruction
  Gaming
  Virtual environments and virtual tourism
  Earth observation
  Archaeology
  Augmented reality
  Reverse engineering
  Motion capture
  3D object recognition, gesture recognition and hand tracking
  Problem Statement:
  Mostly algorithms available for 3D reconstruction are extremely slow and cannot be used in real-time. Though the algorithms presented are still in infancy but they have the potential for fast computation.
  Existing Approaches:
  Delaunay and alpha-shapes
  Delaunay method involves extraction of tetrahedron surfaces from initial point cloud. The idea of ‘shape’ for a set of points in space is given by concept of alpha-shapes. Given a finite point set S, and the real parameter alpha, the alpha-shape of S is a polytope (the generalization to any dimension of a two dimensional polygon and a three-dimensional polyhedron) which is neither convex nor necessarily connected. For a large value, the alpha-shape is identical to the convex-hull of S. The algorithm proposed by Edelsbrunner and Mucke eliminates all tetrahedrons which are delimited by a surrounding sphere smaller than α. The surface is then obtained with the external triangles from the resulting tetrahedron.
  Another algorithm called Tight Cocone labels the initial tetrahedrons as interior and exterior. The triangles found in and out generate the resulting surface.
  Both methods have been recently extended for reconstructing point clouds with noise. In this method the quality of points determines the feasibility of the method. For precise triangulation since we are using the whole point cloud set, the points on the surface with the error above the threshold will be explicitly represented on reconstructed geometry.
  Zero set Methods
  Reconstruction of the surface is performed using a distance function which assigns to each point in the space a signed distance to the surface S. A contour algorithm is used to extracting a zero-set which is used to obtain polygonal representation of the object. Thus, the problem of reconstructing a surface from a disorganized point cloud is reduced to the definition of the appropriate function f with a zero value for the sampled points and different to zero value for the rest. An algorithm called marching cubes established the use of such methods. There are different variants for given algorithm, some use a discrete function f, while other use a polyharmonic radial basis function is used to adjust the initial point set. Functions like Moving Least Squares, basic functions with local support, based on the Poisson equation have also been used. Loss of the geometry precision in areas with extreme curvature, i.e., corners, edges is one of the main issues encountered. Furthermore, pretreatment of information, by applying some kind of filtering technique, also affects the definition of the corners by softening them. There are several studies related to post-processing techniques used in the reconstruction for the detection and refinement of corners but these methods increase the complexity of the solution. 
  VR Technique
  Entire volume transparence of the object is visualized using VR technique. Images will be performed by projecting rays through volume data. Along each ray, opacity and color need to be calculate
caption: Solid geometry with volume rendering Image courtesy of Patrick Chris Fragile Ph.D., UC Santa Barbara
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