2 PATH PLANNING Presented by : Mohamadreza Negahdar Supervisor : Dr. AhmadianCo-Supervisor : Prof. NavabTehran University of Medical SciencesOctober 5 , 2005Mohamadreza Negahdar hails from Tehran , He is currently pursuing his M.Sc. in Biomedical Engineering at Tehran University of Medical Science (TUMS) , Tehran , Iran . His research interests include Image processing , Wavelet & watermarking , Bioinformatics , Medical decision-making , Fuzzy logic & Neuro-fuzzy , Robotics & tele-surgery , Path planning , Virtual endoscopy , Medical instruments , Astronomy , Musicology and etc. .
3 OUTLINE Introduction Path planning in medicine Automatic path generationSkeleton & skeletonizationSkeletonization techniquesMedical applicationsPath planningRoadmapCell decompositionPotential fieldVirtual endoscopyNavigationApplicationsOur work
4 Introduction How can “see” inside the body to screen and cure? Centerline extraction is the basis to understand three dimensional structure of the organGiven a map and goal location, identify trajectory to reach goal locationStrategic competenceHow do we combine these two competencies, along with localization, and mapping, into a coherent framework?
5 Path Planning in medicine Fly-through and navigationGeneral idea of the shape of the organ wallsDetect an abnormal shapeMaking measurements for locating abnormalitiesComputing local distension and lengthRisk of infection or perforation of the anatomy being examined will be eliminatedDetect an abnormal shape such as an ulcer crack or a protruding bump like a polyp, Virtual pathology
6 Path Planning in medicine Bronchoscopy, Airway analysisColonoscopyEsophagusNeurosurgery, Stereotaxic radiosurgeryLiver surgeryAngiographyNeedle steeringMicro-CT imaging
7 ArchitectureSoftware architecture for virtual endoscopy with automatic path searching for interactive navigation support.
8 Restrictions of manually path planning Very time consumingFrustrating for a novice userNeed to improve the performance and lower the costFor this reason, we provide the surgeon with an automatic path generation.
9 Automatic Path Generation Surgeon loads a 3D modelDefines a start and an end pointProgram returns an optimal path centered inside the modelThe user can fly-through the path and/or edit it manually
12 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
13 SkeletonizationThe 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.
14 Skeleton of object The medial axis from an object called its skeleton Skeleton-based techniques first compute a digital skeleton of the entire treeCenter locus of multi-tangent circles (in 2D) or balls (in 3D)The skeleton represents: local object symmetries, and the topological structure of the object.That inserted within the shape of the object
15 Skeletonization techniques detecting ridges in distance map of the boundary pointscalculating the Voronoi diagram generated by the boundary pointsthe layer by layer erosion called thinning
16 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)methodgeometricaltopologicalDistance transformyesnoVoronoi-skeletonThinning
17 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 distance transformation can be executed in linear (O(n)) time in arbitrary dimensions (where "n" is the number of the image elements (e.g. pixels or voxels)). This method fulfils the geometrical requirement (if an error-free Euclidean distance map is calculated), but the topological correctness is not guaranteed.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.)
18 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)
19 Voronoi DiagramThe 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).
20 Voronoi DiagramThe Voronoi diagrams can be computed by an incremental construction:Both requirements (i.e, the topological and the geometrical) can be fulfilled by the skeletonization based on Voronoi diagrams, but it is an expensive process, especially for large and complex objects.If the density of boundary points (as generating points) goes to infinity then the corresponding Voronoi diagram converges to the skeleton.
21 Voronoi SkeletonThe skeleton (marked by red lines) is approximated by a subgraph of the Voronoi diagramSome border points of a rectangle form the set of generating points
22 ThinningBorder 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 easilyThe darkest voxels belong to the computed skeleton.It don’t work at interactive speeds on large database,
24 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 objectIt produces one pixel/voxel width "skeleton“It does not preserve the topology, sincean object is disconnectedan object is completely deletedcavity (white connected component surrounded by an object) is created/a hole is createda cavity/hole is merged with the backgroundtwo cavities/four holes are mergedTopological thinning is an excellent method to reduce the complexity of a model by extraction its skeleton.Example of a 2D reduction operation that does not preserve the topologyExample of a 3D reduction operation that does not preserve the topology
25 Thinningfinding the central path is based on the medial axis of the object. For example, here is a typical colon with the medial axis represented as points:
26 shape preserving thinning The original object (top) and the result of the thinning (bottom). The text remains readable
27 Example of 2D thinning Example of 3D thinning A segmented human ventricle as an original object (left) and its medial lines (right)
28 Medical Applications assessment of laryngotracheal stenosis assessment of infrarenal aortic aneurysmunravelling the colonEach of the emerged three applications requires the cross-sectional profiles of the investigated tubular organsThe skeletonization has been successfully applied in the following three medical applicationsColon Centreline Calculation for CT Colonography using Optimised 3D Topological Thinning
29 Procedure image acquisition by Spiral Computed Tomography (S-CT) (semiautomatic snake-based) segmentation (i.e., determining a binary object from the gray-level picturemorphological filtering of the segmented objectcurve thinning (by using one of our 3D thinning algorithm)raster-to-vector conversionpruning the vector structure (i.e., removing the unwanted branches)smoothing the resulted central pathcalculation of the cross-sectional profile orthogonal to the central path
30 Assessment of LTSThe 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).Many conditions can lead to laryngotracheal stenosis (LTS), most frequent endotracheal intubation, followed by external trauma, or prior airway surgery. Clinical management of these stenosis requires exact information about the number, grade, and the length of the stenosisSite of LTS, length and degree could be depicted on the URT cross-sectional chartsThe segmented URT, its central path, and its cross--sectional profile at the three landmarks (vocal cords, caudal border of the cricoid cartilage, and cranial border of the sternum) and at the narrowest position (top); the line chart (bottom).Cohen's Kappa :Application: This statistic is used to assess inter-rater reliability when observing or otherwise coding qualitative/ categorical variables.Kappa is considered to be an improvement over using % agreement to evaluate this type of reliability.Interpreting Kappa: Kappa has a range from , with larger values indicating better reliability. Generally, a Kappa > .70 isconsidered satisfactory.The segmented URT, its central path
31 Assessment of AAAAlong 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.AAA are abnormal dilatations of the main arterial abdominal vessel due to atherosclerosis. AAA can be found in 2% of people older than 60 years. If the diameter is more than 5 cm than the person is at high risk for AAA rupture, which leads to death in 70-90%. For therapy two main options exist: surgery or endoluminal repair with stentgrafts.In order to investigate the correctness of the applied 3D thinning algorithms, some mathematical phantoms were created.The segmented part of the infrarenal aorta , its central pathTwo phantoms and their central paths
32 Unravelling the ColonUnravelling 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.
33 Unravelling the ColonThe 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).
34 PATH PLANNING Approaches; Roadmap Cell decomposition Potential field road map using Meadow mapsroad map using visibility graphroad map using Voronoi diagramRRTCell decompositionexact cell decompositionapproximate cell decompositionadaptive cell decompositionPotential fieldThe path planning consists of three approaches;Representation of the environment by a road-map (graph), cells or a potential field. The resulting discrete locations or cells allow then to use standard planning algorithms
35 Roadmap Building a network connection between the vertices of polygons Typically represent obstacles as polygons, and the camera as a pointAppropriate for polygon-based dataset , has limitation in VC
36 Path planning: road maps using Meadow maps Use a-priori map, transform free space into convex polygons, grow obstacles by robot sizeConstruct path through polygon edges, from start to goal
37 Path planning: road maps using Meadow maps Polygon generation is computationally complexUses map artifacts to determine polygonsJagged paths - though can fix with path relaxationHow update map if robot discovers discrepancies
38 Path RelaxationPath Relaxation is a method of planning safe paths around obstacles for mobile robots.It works in two steps:a global grid search that finds a rough path,followed by a local relaxation step that adjusts each node on the path to lower the overall path cost.The representation used by Path Relaxation allows an explicit trade off among length of path, clearance away from obstacles, and distance traveled through unmapped areas.
39 Path Relaxation Path Relaxation Property Proof Let p = v0, v1, , vk be a shortest path from s = v0 to vk .If we relax, in order, (v0, v1), (v1, v2), , (vk-1, vk), even intermixed with other relaxations, then d [vk ] = δ(s, vk ).ProofInduction to show that d[vi ] = δ(s, vi ) after (vi-1, vi ) is relaxed.Basis: i = 0. Initially, d [v0] = 0 = δ(s, v0) = δ(s, s).Inductive step:Assume d[vi-1] = δ(s, vi-1).Relax (vi-1, vi ).By convergence property, d [vi ] = δ(s, vi ) afterwardand d [vi ] never changes.
40 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 polygonsFinds shortest sequence of roads from start to goal
41 Path planning: road map using visibility graph Brings robot very close to objectsGenerates shortest path lengthFairly simple implementationInefficient in densely populated environmentsHave to grow obstacles by robot size, sometimes significantly more than robot’s radiusCreate visibility graphPlan shortest path
42 Path planning: road map using Voronoi diagram Edges/roads formed by points that are equidistant from two or more obstaclesFinds shortest sequence of roads from start to goal
43 Path planning: road map using Voronoi diagram Tends to maximize distance from obstaclesCan be a problem for short-range sensors if they can not detect the obstacles, and hence the robot can not localizeNo need to grow obstacles as robot stays “in the middle”Important advantage is that the control system using range sensors can follow Voronoi lines directlyMaximize the readings of local minima in current sensor valuesCan be used to actually create Voronoi diagrams of unknown environments
48 Cell decompositionDivide space into simple connected regions called cellsConstruct connectivity graph from adjacent open cellsFind cells containing start and goal locations, and search for path between them in the connectivity graphCompute path within each cell found in path above, e.g.Pass through midpoints of cell boundariesSequence of wall-following motions and straight line movementsDecomposition of the whole free space into small regions, called cells,
49 Path planning: exact cell decomposition Computational complexity directly depends on density and complexity of elements in environmentSparse is good, even for very geometrically large areas
50 Path planning: approximate cell decomposition Popular due to popularity of grid-based mapsLow computational complexityPotentially large memory requirementsAn approximation cell-decomposition method is often used to improve computational speed by searching for multiresolution dataset , this path planning also has limitation in virtual colonoscopy.
51 Path planning: approximate cell decomposition NF1, ‘grassfire’, algorithmMinima-freeWavefront expansion from goal outwardsEach cell visited once - computational complexity linear in number of cells, not environment complexityNF! (wave propagation)
53 Potential fieldThis approaches is simplified to a point such as a camera model in computer graphicsThe camera moves under the influence of a set of potentials produced by the attraction and repulsion potentialsThe attraction potential pulls robot toward the goal and the repulsion potential pushes it away from the obstaclesThe variation of potentials create the attraction and repulsion forcesComputationally efficient ..
54 Path planning: potential fields Create an artificial field on robot’s map, and treatRobot as point under influence of fieldGoal as the low point (attractive force)Obstacles as peaks (repulsive forces)Generated robot movement is similar to a ball rolling down the hillGoal generates attractive forceObstacle are repulsive forces
55 Potential Field Generation Generation of potential field function U(q)attracting (goal) and repulsing (obstacle) fieldssumming up the fieldsfunctions must be differentiableGenerate artificial force field F(q)Set robot speed (vx, vy) proportional to the force F(q) generated by the fieldthe force field drives the robot to the goalif robot is assumed to be a point mass
56 Attractive Potential Field Parabolic function representing the Euclidean distance to the goalAttracting force converges linearly towards 0 (goal)
57 Repulsion Potential Field Should generate a barrier around all the obstaclestrong if close to the obstaclenot influence if far from the obstacle: minimum distance to the objectField is positive or zero and tends to infinity as q gets closer to the object
58 Path planning: potential fields Fairly easy to implementSet robot speed proportional to forceField drives robot to the goalMovement is similar to a ball rolling down a hillIs also a control law as robot can always determine next required action (assuming robot can localize position with respect to its map and the field)Local minima can be problematicConcave objects can generate oscillationsMore complicated if robot is not treated as point massComputationally efficient ...Major drawback : the robot can stuck in local minima. One way to solve this problem is to design potential without local minima, the other is to design powerful mechanisms to escape from local minima.If objects are convex there exists situations where several minimal distances exist ® can result in oscillations
59 Path planning: potential field, extensions Rotation potential fieldRepulsive force also a function of orientation, e.g. an obstacle parallel to robot’s direction of travelEnhanced wall following
60 Virtual Endoscopy - Idea Input a high-resolution 3D radiologic imagevirtual copy of anatomyUse computer to explore virtual anatomypermits unlimited navigation explorationCompact and Intuitive way to explore huge amount of informationIn each frame, the view on the left is the virtual CT rendering and on the right is the endoscope image
61 NavigationThe camera automatically moves from the source point towards the target pointUser can interactively modified the camera position and directionThe camera stays away from the surfaceThe camera should never penetrate through the surfaceThe physician can change source and target positionsEssentially, there are three groups of camera control techniques: manual, planned and guided navigation.
62 Virtual Navigator - Architecture The physician applies the Virtual Navigator in two Stages. In Stage 1, the physician uses a 3D CT scan to identify target biopsy sites, construct the main airway tree, and define centerline paths through the major airways. This information is stored in a Case Study. Later, during Stage 2 Live Bronchoscopy, the Virtual Navigator is interfaced directly to the bronchoscope. The case study information is used during live bronchoscopy to help guide biopsy.
64 Gheorghe Iordanescu, PhD, Ronald M. Summers, MD, PhD Virtual colonoscopysimplification of the colonic surface by decimationthinning of the decimated colon to create a preliminary centerlineselection of equally spaced points on the preliminary centerlinegrouping neighboring pointsmapping them back to rings in the original colonCenterlineComputed tomography colonography (CTC)Gheorghe Iordanescu, PhD, Ronald M. Summers, MD, PhD
65 Virtual colonoscopy184.108.40.206.5.6.Centerline computationFinal remappingstartdecimationthinningmodelingremappingStart: The starting point is the original colon surface (SOC), produced from the CTC images using a region growing segmentation and isosurface extraction. The threshold for the isosurface extraction is a specific Hounsfield unit (HU). The “marching cubes” algorithm was used to extract the isosurface. The surface is composed of many small triangles, which are described by their vertices and edges.Decimation: The SOC is simplified using decimation to minimize the number of operations performed in subsequent steps. Decimation keeps the general appearance and topology of the colon but reduce the number of vertices in region of the surface with low curvature. The result of this step is the decimated colon surface (SDC).Flowchart of the centerline computation algorithm.we seek to find an ordered set of 3D points that define the colon’s centerline.vertices are described using the notation V[i].Start : Colon surface SOCDecimation : SOC -> SDCGheorghe Iordanescu, PhD, Ronald M. Summers, MD, PhD
66 Virtual colonoscopy220.127.116.11.5.6.Centerline computationFinal remappingstartdecimationthinningmodelingremappingThinning: We compute the thinned colon surface (STC) by iteratively averaging the distances between colon vertices in the SDC.The thinning is equivalent to applying a Laplacian operator to each vertex V[i]. If vertex V[i] has N[i] neighbors and all of these neighbors are in a neighborhood Ni, the formula for thinning is:vertices are described using the notation V[i].The main effect of applying the Laplacian operator is a shrinkage of the local colon diameter. There are two side effects of thinning: tight loops are smoothed and the entire colon is compressed slightly. Both side effects are corrected in the remapping step.The number of vertices does not change by thinning. SDC and STC have the same number of vertices and the same vertex connectivity.Thinning : SDC -> STCThinning evolution of a 3D colon surface (a) Three-dimensional surface of the human colon reconstructed from a CT colonography dataset. (b) Thinned 3D surface of the human colon; 250 (dark red), 500 (green), and 1,000 (blue) iterations.Gheorghe Iordanescu, PhD, Ronald M. Summers, MD, PhD
67 Virtual colonoscopy18.104.22.168.5.6.Centerline computationFinal remappingstartdecimationthinningmodelingremappingModeling: We create a model of the STC by taking equally spaced vertices from the STC. The model of the STC will be composed of straight segments that connect these approximately equally spaced vertices from the STC. To obtain the correct vertices, we use a region growing strategy in which we start from a seed point and identify vertices connected to the seed.Flowchart of the centerline computation algorithm.Modeling the colon by an ordered set of 3D point. (a) Portion of the thinned colon, its vertices (red crosses) and their connectivity are displayed. (b) Some vertices are selected to model the thinned colon (green circles). (c) Model of the tinned colon, piece-wise linear curve instead of a surface mesh (d) Portion of the tinned colon and its piece-wise linear model.Gheorghe Iordanescu, PhD, Ronald M. Summers, MD, PhD
68 Virtual colonoscopy22.214.171.124.5.6.Centerline computationFinal remappingstartdecimationthinningmodelingremappingRemapping: We use the model to compute slices through the STC that correspond to rings in the SDC. Using the one-to-one mapping of the vertices on the STC and SDC, the indices of the vertices from the same slice in the STC are used to get a ring in the SDC.The result is vertices from the SDC that are grouped in ring-like areas, where each ring is approximately perpendicular to the colon centerline.Flowchart of the centerline computation algorithm.Remapping : STC -> SDCSteps in the centerline algorithm. (a) Original 3D colonic surface from prone CTC. (b) Blue curve shows the preliminary centerline after thinning and modeling. Preliminary centerlines may not lie within the colonic lumen. Green curve shows the final centerline after remapping. The final centerline lies within the colonic lumen. (c) Detail of sigmoid colon (blue box in (a)). (d) Segmented colon. Colon rings (cross-sections) are colored.Gheorghe Iordanescu, PhD, Ronald M. Summers, MD, PhD
69 Virtual colonoscopy126.96.36.199.5.6.Centerline computationFinal remappingstartdecimationthinningmodelingremappingCenterline Computation: The centers-of-mass of the edges of adjacent rings of the SDC is the local centerline point. We determine the local centerline point by averaging the vertices at the rings’ edges. The resulting points at the center of each ring are again interpolated for purpose of display using spline functions. The ring centers and interpolated points constitute the final centerline. For interpolation we use the Catmull-Rom spline.Flowchart of the centerline computation algorithm.Detail of the centerline in different colonic segments. Portions of the (a) splenic flexure, (b) hepatic flexure, and (c) transverse colon are shown.Gheorghe Iordanescu, PhD, Ronald M. Summers, MD, PhD
70 Catmull-Rom SpilnesSplines are a mathematical means of representing a curve, by specifying a series of points at intervals along the curve and defining a function that allows additional points within an interval to be calculated.The points that define a spline are known as "Control Points". One of the features of the Catmull-Rom spline is that the specified curve will pass through all of the control points - this is not true of all types of splines.To calculate a point on the curve, two points on either side of the desired point are required, as shown on the next. The point is specified by a value t that signifies the portion of the distance between the two nearest control points.
71 Catmull-Rom SpilnesGiven the control points P0, P1, P2, and P3, and the value t, the location of the point can be calculated as (assuming uniform spacing of control points):[ ] [P0][ ] [P1]q(t) = 0.5 * (1.0f, t, t^2, t^3) * *[ ] [P2][ ] [P3]To put that another way:q(t) = 0.5( (2 * P1) + (-P0 + P2) * t + (2*P0 – 5*P1 + 4*P2 – P3) * t^ (-P0 + 3P1 – 3*P2 = P3) * t^3 )
72 Catmull-Rom SpilnesThis formula gives Catmull-Rom spline the following characteristics:The spline passes through all of the control points.The spline is C1 continuous, meaning that there are no discontinuities in the tangent direction and magnitude.The spline is not C2 continuous. The second derivative is linearly interpolated within each segment, causing the curvature to vary linearly over the length of the segment.Points on a segment may lie outside of the domain of P1 -> P2.While a spline segment is defined using four control points, a spline may have any number of additional control points. This results in a continuous chain of segments, each defined by the two control points that form the endpoints of the segments, plus an additional control point on either side of the endpoints. Thus for a given segment with endpoints Pn and Pn+1, the segment would be calculated using [Pn-1, Pn, Pn+1, Pn+2].Because a segment requires control points to the outside of the segment endpoints, the segments at the extreme ends of the spline cannot be calculated. Thus, for a spline with control points 1 through N, the minimum segment that can be formulated is P1<->P2, and the maximum segment is PN-3<->PN-2. Thus, to define S segments, S+3 control points are required
73 Virtual colonoscopy188.8.131.52.5.6.Centerline computationFinal remappingstartdecimationthinningmodelingremappingMapping the SDC to the SOC: A second mapper associates vertices in the SDC with the vertices in the SOC based on minimum distance criterion between the vertices of the two surfaces. Based on the correspondence of the vertices on the SDC and SOC we can segment the SOC and split the surface into rings.To limit the search space and improve computational efficiency in performing this second mapping , a process called “vertex classification” is performed, vertices in the SDC and SOC are grouped into classes according to their spatial coordinates. Because only vertices in neighboring classes need to be searched, there is a substantial performance improvement.The centerline of the SOC is the same as the centerline of the SDC.Applications: The utility of the centerline was shown for two applications. First, the volume of each ring was used to quantify local colonic distension. Second, the normalized distance along the centerline (NDAC) was computed and compared for a series of polyps seen on both the prone and supine examinations.Gheorghe Iordanescu, PhD, Ronald M. Summers, MD, PhD
75 Virtual Endoscopy (based on potential fields) The idea is to utilize a hierarchical analysis of attractors to determine principal attractorsWe combine potentials derived from the distance between source and target positions and from the distance to the colon surface to guide path search process, the paths far away from the colon wall and in the direction of target positionAdvantages:Eliminating small-undesired branches during the attractor analysis.Warranty of connectivity between start and target points.Search of paths just between principal attractors and do not waste time in connecting the small attractors.Pre-processing (skeleton & potential field generation),Skeleton simplification to eliminate excessive ramification,Perform the simplification before the skeleton generation,These potentials are essential to obtain priority in choosing the paths far away from colon wall and in the direction of target position,The attraction potential pulls robot toward the goal and the repulsion potential pushes it away from the obstacles.Rui C. H. Chiou, Arie E. Kaufman, Zhengrong Liang, Lichan Hong and Miranda Achniotou
76 Virtual Endoscopy (based on potential fields) Calculate distance from surface and targetDetect attractorsAnalyze hierarchical attractorsAnalyze attractors according to their contribution to principal skeletonCalculate distance from next consecutive principal attractorThe idea is to take the most powerful attractor and scan its influence zone by 3D distance region growingThe process repeats for the next most powerful attractor until the source target principal attractors are foundSearch paths between principal attractorsWe model DFSfc as waves which propagate from the surface into the center of attraction with progressing intensity, the center of attraction is a point with maximum intensity.A skeleton with peripheral ramifications do not desirable under a navigation view point.the principal attractors are the minimal attractors with maximal power required to satisfy the connectivity criterion.The idea is to take the most powerful attractor and scan its influence zone by 3D distance region growing,The process repeats for the next most powerful attractor until the source target principal attractors are found,It is very difficult for the user to find the principal attractors by interaction.Once the principal attractors are searched we need to connect them to obtain the principal skeleton.Rui C. H. Chiou, Arie E. Kaufman, Zhengrong Liang, Lichan Hong and Miranda Achniotou
78 Virtual BronchoscopyVB is a computer-based approach for navigating virtually through airways captured in a 3-D MDCT imageVB 3-D image analysis:Guidance of bronchoscopyHuman lung-cancer assessmentPlanning and guiding bronchoscopic biopsiesQuantitative airway analysis –noninvasively-Smooth virtual navigationA suitable method must:Provide a detailed, smooth structure of the airway tree’s central axesRequire little human interactionFunction over a wide range of conditions as observed in typical lung-cancer patientsMultidetector computed-tomography (MDCT)The advantage of VB is that airway analysis can be done noninvasively, thus enabling more careful assessment and follow-on procedure planning.Local measurements on airway branchesA. P. Kiraly, J. P. Helferty, E. A. Hoffman, G. McLennan, and W. E. Higgins
79 Virtual BronchoscopyA major component of path planning system for VB is a method for computing the central airway paths (centerlines) from a 3-D MDCT chest imageThe method:Define the skeleton of a given segmented 3-d chest imagePerform a multistage refinement of the skeleton to arrive at a final tree structureA. P. Kiraly, J. P. Helferty, E. A. Hoffman, G. McLennan, and W. E. Higgins
80 Virtual Bronchoscopy Quicksee-Basic operation: Load Data 3D radiologic imageDo Automatic AnalysisComputePaths (axes) through airwaysExtract regions (airways)Save results for interactive navigationPerform Interactive navigation/assessmentView, Edit, create paths through 3D imageView structure; get quantitative dataMany visual aids and viewers availableA. P. Kiraly, J. P. Helferty, E. A. Hoffman, G. McLennan, and W. E. Higgins
81 Segmented Airway Tree IS and Root Site Virtual BronchoscopyStage 1:3D SkeletonizationSegmented Airway Tree IS and Root SiteStage 2:1. Length-based Elimination2. Simple Centering3. Line-based Elimination4. Sphere-based EliminationStage 3:1. Site Elimination2. Sub-voxel Centering3. Spline FittingA presegmented 3-D image IS , containing a branching tree structure of interest, and a preselected root site denoting the approximate starting location of the tree, serve as inputs. The goal is to produce a description of the tree’s branch structure suitable for navigation and quantitative analysis.Stage 4:Direction SettingFinal TreeT = (V,B,P)A. P. Kiraly, J. P. Helferty, E. A. Hoffman, G. McLennan, and W. E. Higgins
82 3D Airway Segmentation Overview 3D imageIModified 3D Region GrowingOptional FilterLung Region DefinitionOptional FilterThis shows an overview of the segmentation methodMorphology2D Candidate Labeling3D ReconstructionAirway SegmentationIS
83 Virtual BronchoscopyA. P. Kiraly, J. P. Helferty, E. A. Hoffman, G. McLennan, and W. E. Higgins
84 OUR WORKGoals:The aim of our work is to build trajectories for virtual endoscopy inside 3D medical images, using the most automatic way.Virtual endoscopy results are shown in various anatomical regions (bronchi, colon, brain vessels, arteries) with different 3D imaging protocols (CT, MR).In my thesis, an automatic centerline determination algorithm for three dimensional virtual bronchoscopy CT image will be present.We try that our method:Be fasterNeeds less interactionBe more robust and reproducibleis faster: computing time is below the minute on a standard PCneeds less interaction: only one user defined point needed for the complete trajectoryis more robust and reproducible: segment and compute the trajectory at the same time, dos not rely on a previously segmented object.
88 Discussion email@example.com firstname.lastname@example.org Questions …. Suggestions …. Comments …. Ideas …. ?This presentation designed and presented by Mohamadreza Negahdar at Tehran University of Medical Science (TUMS).,