1 / 77

PATH PLANNING

PATH PLANNING. Presented by : Mohamadreza Negahdar Supervisor : Dr. Ahmadian Co-Supervisor : Prof. Navab Tehran University of Medical Sciences October 5 , 2005. OUTLINE. Introduction Path planning in medicine Automatic path generation Skeleton & skeletonization

wind
Download Presentation

PATH PLANNING

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. PATH PLANNING Presented by : Mohamadreza Negahdar Supervisor : Dr. Ahmadian Co-Supervisor : Prof. Navab Tehran University of Medical Sciences October 5 , 2005

  2. OUTLINE • Introduction • Path planning in medicine • Automatic path generation • Skeleton & skeletonization • Skeletonization techniques • Medical applications • Path planning • Roadmap • Cell decomposition • Potential field • Virtual endoscopy • Navigation • Applications • Our work

  3. Introduction • How can “see” inside the body to screen and cure? • Centerline extraction is the basis to understand three dimensional structure of the organ • Given a map and goal location, identify trajectory to reach goal location • Strategic competence • How do we combine these two competencies, along with localization, and mapping, into a coherent framework?

  4. Path Planning in medicine • Fly-through and navigation • General idea of the shape of the organ walls • Detect an abnormal shape • Making measurements for locating abnormalities • Computing local distension and length • Risk of infection or perforation of the anatomy being examined will be eliminated

  5. Path Planning in medicine • Bronchoscopy, Airway analysis • Colonoscopy • Esophagus • Neurosurgery, Stereotaxic radiosurgery • Liver surgery • Angiography • Needle steering

  6. Architecture

  7. Restrictions of manually path planning • Very time consuming • Frustrating for a novice user • Need to improve the performance and lower the cost • For this reason, we provide the surgeon with an automatic path generation.

  8. Automatic Path Generation • Surgeon loads a 3D model • Defines a start and an end point • Program returns an optimal path centered inside the model • The user can fly-through the path and/or edit it manually

  9. Input

  10. Output

  11. Automatic Path Planning for VE • The goal is to automatically extract a fly-through trajectory for the endoscope that stays as far as possible from the organ walls in order to maximize the amount of information that the user sees during the fly-through

  12. Skeletonization • The aim of the skeletonization is to extract a region-based shape feature representing the general form of an object. • We have applied skeletonization to extract the central path of a 3D "tubular" object.

  13. Skeleton of object • The medial axis from an object called its skeleton • Skeleton-based techniques first compute a digital skeleton of the entire tree • Center locus of multi-tangent circles (in 2D) or balls (in 3D) • The skeleton represents: local object symmetries, and the topological structure of the object.

  14. Skeletonization techniques • detecting ridges in distance map of the boundary points • calculating the Voronoi diagram generated by the boundary points • the layer by layer erosion called thinning

  15. Comparison of Skeletonization Techniques • In digital spaces, only an approximation to the "true skeleton" can be extracted. There are two requirements to be complied with: • topological (to retain the topology of the original object) • geometrical (forcing the "skeleton" being in the middle of the object and invariance under the most important geometrical transformation including translation, rotation, and scaling)

  16. Distance Transformation • The original (binary) image is converted into feature and non-feature elements. The feature elements belong to the boundary of the object. • The distance map is generated where each element gives the distance to the nearest feature element. • The ridges (local extremes) are detected as skeletal points. • The distance map resulted by the distance transformation depends on the chosen distance . The original binary object (left) and its distance map (right). (The distance map is displayed as a surface where the ridge points belong to the skeleton.)

  17. Distance Transformation • Chose of distance: Extracted feature points (left) and distance map using city block (or 4-neighbour) distance (right) Distance map using chess-board (or 8-neighbour) distance (left) and distance map using (3,4)-chamfer distance (right)

  18. Voronoi Diagram • The Voronoi diagram of a discrete set of points (called generating points) is the partition of the given space into cells so that each cell contains exactly one generating point and the locus of all points which are nearer to this generating point than to other generating points. The 10 generating points (left) and their Voronoi diagram (right).

  19. Voronoi Diagram • The Voronoi diagrams can be computed by an incremental construction: If the density of boundary points (as generating points) goes to infinity then the corresponding Voronoi diagram converges to the skeleton.

  20. Voronoi Skeleton The skeleton (marked by red lines) is approximated by a subgraph of the Voronoi diagram Some border points of a rectangle form the set of generating points

  21. Thinning • Border points of a binary object are deleted in iteration steps until only the “skeleton” is left. • In case of “near tubular” 3D objects (e.g., airway, blood vessel, and gastro–intestinal tract), Thinning has a major advantage over the other skeletonization methods since curve thinning can produces medial lines easily

  22. Thinning

  23. Thinning • The thinning has some beneficial properties: • It preserves the topology (retains the topology of the original object) • It preserves the shape (significant feature suitable for object recognition or classification is extracted) • It forces the "skeleton" being in the middle of the object • It produces one pixel/voxel width "skeleton“ • It does not preserve the topology, since • an object is disconnected • an object is completely deleted • cavity (white connected component surrounded by an object) is created/a hole is created • a cavity/hole is merged with the background • two cavities/four holes are merged

  24. Thinning

  25. Medical Applications • assessment of laryngotracheal stenosis • assessment of infrarenal aortic aneurysm • unravelling the colon • Each of the emerged three applications requires the cross-sectional profiles of the investigated tubular organs

  26. Procedure • image acquisition by Spiral Computed Tomography (S-CT) • (semiautomatic snake-based) segmentation (i.e., determining a binary object from the gray-level picture • morphological filtering of the segmented object • curve thinning (by using one of our 3D thinning algorithm) • raster-to-vector conversion • pruning the vector structure (i.e., removing the unwanted branches) • smoothing the resulted central path • calculation of the cross-sectional profile orthogonal to the central path

  27. Assessment of LTS • The cross-sectional profiles (based on the central path) of the upper respiratory tract (URT) were calculated with proven LTS on fiberoptic endoscopy (FE). • Locations of LTS were determined on axial S-CT slices and compared to findings of fiberoptic endoscopy (FE) by Cohen's kappa statistics. Regarding the site of LTS an excellent correlation was found between FE and S-CT (z=7.44, p<0.005). The segmented URT, its central path

  28. Assessment of AAA • Along the central path the cross-sectional profile was computed. • The maximum diameter in 3D as well as the length of the proximal and distal neck of the aneurysma , Since size of the aneurysma is regarded to be a prognosticated factor. • The volume of the segmented aneurysma was determined too. The segmented part of the infrarenal aorta , its central path Two phantoms and their central paths

  29. Unravelling the Colon • Unravelling the colon is a new method to visualize the entire inner surface of the colon without the need for navigation. • This is a minimally invasive technique that can be used for colorectal polyps and cancer detection. • An algorithm for unravelling the colon which is to digitally straighten and then flatten using reconstructed spiral/helical computer tomograph (CT) images. • Comparing to virtual colonoscopy where polyps may be hidden from view behind the folds, the unravelled colon is more suitable for polyp detection, because the entire inner surface is displayed at one view.

  30. Unravelling the Colon The segmented volume of a part of the artificial phantom with two polyps (top) and the same part of the phantom after unravelling (bottom). The segmented volume of a part of the cadavric phantom with polyps (top) and the unravelled colon (bottom).

  31. PATH PLANNING • Approaches; • Roadmap • road map using Meadow maps • road map using visibility graph • road map using Voronoi diagram • RRT • Cell decomposition • exact cell decomposition • approximate cell decomposition • adaptive cell decomposition • Potential field

  32. Roadmap • Building a network connection between the vertices of polygons • Typically represent obstacles as polygons, and the camera as a point • Appropriate for polygon-based dataset , has limitation in VC

  33. Path planning: road maps using Meadow maps • Use a-priori map, transform free space into convex polygons, grow obstacles by robot size • Construct path through polygon edges, from start to goal

  34. Path planning: road maps using Meadow maps • Polygon generation is computationally complex • Uses map artifacts to determine polygons • Jagged paths - though can fix with path relaxation • How update map if robot discovers discrepancies

  35. Path planning: road map using visibility graph • Consists of edges/roads joining all pairs of vertices that can see each other (including start and goal positions) • Implies edges along the side of polygons • Finds shortest sequence of roads from start to goal

  36. Path planning: road map using visibility graph • Brings robot very close to objects • Generates shortest path length • Fairly simple implementation • Inefficient in densely populated environments Create visibility graph Plan shortest path

  37. Path planning: road map using Voronoi diagram • Edges/roads formed by points that are equidistant from two or more obstacles • Finds shortest sequence of roads from start to goal

  38. Path planning: road map using Voronoi diagram • Tends to maximize distance from obstacles • Can be a problem for short-range sensors if they can not detect the obstacles, and hence the robot can not localize • No need to grow obstacles as robot stays “in the middle” • Important advantage is that the control system using range sensors can follow Voronoi lines directly • Maximize the readings of local minima in current sensor values • Can be used to actually create Voronoi diagrams of unknown environments

  39. Voronoi diagram

  40. Rapidly-exploring Random trees • Begin at the start state • Attempt to grow into the goal state • By exploring the vehicle’s state space • Search from both sides Goal Start

  41. RRT

  42. RRT

  43. Cell decomposition • Divide space into simple connected regions called cells • Construct connectivity graph from adjacent open cells • Find cells containing start and goal locations, and search for path between them in the connectivity graph • Compute path within each cell found in path above, e.g. • Pass through midpoints of cell boundaries • Sequence of wall-following motions and straight line movements

  44. Path planning: exact cell decomposition • Computational complexity directly depends on density and complexity of elements in environment • Sparse is good, even for very geometrically large areas

  45. Path planning: approximate cell decomposition • Popular due to popularity of grid-based maps • Low computational complexity • Potentially large memory requirements

  46. Path planning: approximate cell decomposition • NF1, ‘grassfire’, algorithm • Minima-free • Wavefront expansion from goal outwards • Each cell visited once - computational complexity linear in number of cells, not environment complexity

  47. Path planning: adaptive cell decomposition

  48. Potential field • This approaches is simplified to a point such as a camera model in computer graphics • The camera moves under the influence of a set of potentials produced by the attraction and repulsion potentials • The attraction potential pulls robot toward the goal and the repulsion potential pushes it away from the obstacles • The variation of potentials create the attraction and repulsion forces

  49. Path planning: potential fields • Create an artificial field on robot’s map, and treat • Robot as point under influence of field • Goal as the low point (attractive force) • Obstacles as peaks (repulsive forces)

More Related