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In the name of God …

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**PATH PLANNING Presented by : Mohamadreza Negahdar**

Supervisor : Dr. Ahmadian Co-Supervisor : Prof. Navab Tehran University of Medical Sciences October 5 , 2005 Mohamadreza 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. .

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**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

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**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?

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**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 Detect an abnormal shape such as an ulcer crack or a protruding bump like a polyp, Virtual pathology

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**Path Planning in medicine**

Bronchoscopy, Airway analysis Colonoscopy Esophagus Neurosurgery, Stereotaxic radiosurgery Liver surgery Angiography Needle steering Micro-CT imaging

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Architecture Software architecture for virtual endoscopy with automatic path searching for interactive navigation support.

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**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.

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**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

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Input

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Output

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**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

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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.

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**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. That inserted within the shape of the object

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**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

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**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) method geometrical topological Distance transform yes no Voronoi-skeleton Thinning

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**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.)

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**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)

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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).

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Voronoi Diagram The 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.

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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

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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 The darkest voxels belong to the computed skeleton. It don’t work at interactive speeds on large database,

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Thinning

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**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 Topological 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 topology Example of a 3D reduction operation that does not preserve the topology

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Thinning finding 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:

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**shape preserving thinning**

The original object (top) and the result of the thinning (bottom). The text remains readable

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**Example of 2D thinning Example of 3D thinning**

A segmented human ventricle as an original object (left) and its medial lines (right)

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**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 The skeletonization has been successfully applied in the following three medical applications Colon Centreline Calculation for CT Colonography using Optimised 3D Topological Thinning

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**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

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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). 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 stenosis Site of LTS, length and degree could be depicted on the URT cross-sectional charts The 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 is considered satisfactory. The segmented URT, its central path

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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. 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 path Two phantoms and their central paths

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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.

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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).

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**PATH PLANNING Approaches; Roadmap Cell decomposition Potential field**

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 The 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

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**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

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**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

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**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

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Path Relaxation Path 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.

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**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 ). Proof Induction 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 ) afterward and d [vi ] never changes.

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**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

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**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 Have to grow obstacles by robot size, sometimes significantly more than robot’s radius Create visibility graph Plan shortest path

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**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

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**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

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Voronoi diagram

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**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

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RRT

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RRT

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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 Decomposition of the whole free space into small regions, called cells,

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**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

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**Path planning: approximate cell decomposition**

Popular due to popularity of grid-based maps Low computational complexity Potentially large memory requirements An 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.

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**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 NF! (wave propagation)

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**Path planning: adaptive cell decomposition**

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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 Computationally efficient ..

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**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) Generated robot movement is similar to a ball rolling down the hill Goal generates attractive force Obstacle are repulsive forces

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**Potential Field Generation**

Generation of potential field function U(q) attracting (goal) and repulsing (obstacle) fields summing up the fields functions must be differentiable Generate artificial force field F(q) Set robot speed (vx, vy) proportional to the force F(q) generated by the field the force field drives the robot to the goal if robot is assumed to be a point mass

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**Attractive Potential Field**

Parabolic function representing the Euclidean distance to the goal Attracting force converges linearly towards 0 (goal)

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**Repulsion Potential Field**

Should generate a barrier around all the obstacle strong if close to the obstacle not influence if far from the obstacle : minimum distance to the object Field is positive or zero and tends to infinity as q gets closer to the object

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**Path planning: potential fields**

Fairly easy to implement Set robot speed proportional to force Field drives robot to the goal Movement is similar to a ball rolling down a hill Is 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 problematic Concave objects can generate oscillations More complicated if robot is not treated as point mass Computationally 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

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**Path planning: potential field, extensions**

Rotation potential field Repulsive force also a function of orientation, e.g. an obstacle parallel to robot’s direction of travel Enhanced wall following

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**Virtual Endoscopy - Idea**

Input a high-resolution 3D radiologic image virtual copy of anatomy Use computer to explore virtual anatomy permits unlimited navigation exploration Compact and Intuitive way to explore huge amount of information In each frame, the view on the left is the virtual CT rendering and on the right is the endoscope image

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Navigation The camera automatically moves from the source point towards the target point User can interactively modified the camera position and direction The camera stays away from the surface The camera should never penetrate through the surface The physician can change source and target positions Essentially, there are three groups of camera control techniques: manual, planned and guided navigation.

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**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.

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APPLICATIONS

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**Gheorghe Iordanescu, PhD, Ronald M. Summers, MD, PhD**

Virtual colonoscopy simplification of the colonic surface by decimation thinning of the decimated colon to create a preliminary centerline selection of equally spaced points on the preliminary centerline grouping neighboring points mapping them back to rings in the original colon Centerline Computed tomography colonography (CTC) Gheorghe Iordanescu, PhD, Ronald M. Summers, MD, PhD

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Virtual colonoscopy 1. 2. 3. 4. 5. 6. Centerline computation Final remapping start decimation thinning modeling remapping Start: 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 SOC Decimation : SOC -> SDC Gheorghe Iordanescu, PhD, Ronald M. Summers, MD, PhD

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Virtual colonoscopy 1. 2. 3. 4. 5. 6. Centerline computation Final remapping start decimation thinning modeling remapping Thinning: 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 -> STC Thinning 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

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Virtual colonoscopy 1. 2. 3. 4. 5. 6. Centerline computation Final remapping start decimation thinning modeling remapping Modeling: 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

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Virtual colonoscopy 1. 2. 3. 4. 5. 6. Centerline computation Final remapping start decimation thinning modeling remapping Remapping: 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 -> SDC Steps 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

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Virtual colonoscopy 1. 2. 3. 4. 5. 6. Centerline computation Final remapping start decimation thinning modeling remapping Centerline 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

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Catmull-Rom Spilnes Splines 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.

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Catmull-Rom Spilnes Given 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 )

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Catmull-Rom Spilnes This 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

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Virtual colonoscopy 1. 2. 3. 4. 5. 6. Centerline computation Final remapping start decimation thinning modeling remapping Mapping 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

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Virtual colonoscopy

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**Virtual Endoscopy (based on potential fields)**

The idea is to utilize a hierarchical analysis of attractors to determine principal attractors We 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 position Advantages: 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

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**Virtual Endoscopy (based on potential fields)**

Calculate distance from surface and target Detect attractors Analyze hierarchical attractors Analyze attractors according to their contribution to principal skeleton Calculate distance from next consecutive principal attractor 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 Search paths between principal attractors We 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

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Virtual Endoscopy

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Virtual Bronchoscopy VB is a computer-based approach for navigating virtually through airways captured in a 3-D MDCT image VB 3-D image analysis: Guidance of bronchoscopy Human lung-cancer assessment Planning and guiding bronchoscopic biopsies Quantitative airway analysis –noninvasively- Smooth virtual navigation A suitable method must: Provide a detailed, smooth structure of the airway tree’s central axes Require little human interaction Function over a wide range of conditions as observed in typical lung-cancer patients Multidetector 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 branches A. P. Kiraly, J. P. Helferty, E. A. Hoffman, G. McLennan, and W. E. Higgins

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Virtual Bronchoscopy A major component of path planning system for VB is a method for computing the central airway paths (centerlines) from a 3-D MDCT chest image The method: Define the skeleton of a given segmented 3-d chest image Perform a multistage refinement of the skeleton to arrive at a final tree structure A. P. Kiraly, J. P. Helferty, E. A. Hoffman, G. McLennan, and W. E. Higgins

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**Virtual Bronchoscopy Quicksee-Basic operation: Load Data**

3D radiologic image Do Automatic Analysis Compute Paths (axes) through airways Extract regions (airways) Save results for interactive navigation Perform Interactive navigation/assessment View, Edit, create paths through 3D image View structure; get quantitative data Many visual aids and viewers available A. P. Kiraly, J. P. Helferty, E. A. Hoffman, G. McLennan, and W. E. Higgins

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**Segmented Airway Tree IS and Root Site**

Virtual Bronchoscopy Stage 1: 3D Skeletonization Segmented Airway Tree IS and Root Site Stage 2: 1. Length-based Elimination 2. Simple Centering 3. Line-based Elimination 4. Sphere-based Elimination Stage 3: 1. Site Elimination 2. Sub-voxel Centering 3. Spline Fitting A 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 Setting Final Tree T = (V,B,P) A. P. Kiraly, J. P. Helferty, E. A. Hoffman, G. McLennan, and W. E. Higgins

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**3D Airway Segmentation Overview**

3D image I Modified 3D Region Growing Optional Filter Lung Region Definition Optional Filter This shows an overview of the segmentation method Morphology 2D Candidate Labeling 3D Reconstruction Airway Segmentation IS

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Virtual Bronchoscopy A. P. Kiraly, J. P. Helferty, E. A. Hoffman, G. McLennan, and W. E. Higgins

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OUR WORK Goals: 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 faster Needs less interaction Be more robust and reproducible is faster: computing time is below the minute on a standard PC needs less interaction: only one user defined point needed for the complete trajectory is more robust and reproducible: segment and compute the trajectory at the same time, dos not rely on a previously segmented object.

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**False branch Elimination**

OUR WORK Method: Skeletonization False branch Elimination and Simple Centering Pre-segmented Airway Tree methodology Tree Refinement Direction Setting Bronchi Tree

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Virtual Bronchoscopy Thomas Deschamps

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Virtual Bronchoscopy Thomas Deschamps

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**Discussion mrnegahdar@razi.tums.ac.ir mrnus@yahoo.com**

Questions …. Suggestions …. Comments …. Ideas …. ? This presentation designed and presented by Mohamadreza Negahdar at Tehran University of Medical Science (TUMS). ,

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DIGITAL IMAGE PROCESSING

DIGITAL IMAGE PROCESSING

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