Image Processing and Image Analysis for
Medical Visualization (II)
Bernhard Preim
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Classification
• Segmentation procedures
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Introduction
Point-oriented Procedures
Edge-oriented Procedures
Region-oriented Procedures
Applications: Segmentation of organs, lesions and vessels
Postprocessing with morphologic operators
Skeletonization
Quantitative analysis of medical image data
Implementation of image processing algorithms
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Introduction
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Segmentation: Introduction
• Goal: Identification of pixels that meet one homogeneity criterion
• Why structures are segmented?
• Selective highlighting and fading of structures, high-quality
visualization
• Basis for a classification (muscles, bones, …)
• Basis for further processing (e.g. skeletonization)
• Basis for a quantitative analysis (volumetry, form-describing
parameters, …)
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Segmentation: Introduction
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Segmentation: Introduction
Quality criteria:
• Precision (comparison with manual segmentation by
human experts)
• Speed determines application areas
(emergency cases, intraoperative use, …)
• Robustness against noise
• impacts of disruptions, such as patient movement, metal artifacts,
influence of variable pathological changes
• Fast feedback
• Reproducibility (example: follow-up during MS lesions)
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Segmentation: Introduction
• Examples: Identification of pathological changes (tumors),
different organs, vessels, bones, catheters, …
• Problem: Suitability of segmentation methods strongly depends
on:
• the applied modalities (CT, MRT, ultrasound, …)
• the specific acquisition parameters (contrast agent
administration, resolution, noise, sequence, …)
• the objects to be detected (thin hierarchical vessels, compact
large organs)
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Segmentation: Introduction
Introduction
• Point-oriented Procedures
• Edge-oriented Procedures
• Region-oriented Procedures
• Model-based Procedures
Homogeneity Critera:
• grey values, gradients, textures
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Segmentation: Point-oriented Procedures
• Pixels are attributed to objects based on the gray value
(thresholding)
• Histogram analysis to identify suitable thresholds (minima)
• Advantage: fast, simple method
• Disadvantage: Neglect of spatial relations
→ postprocessing
• Variations: local threshold methods (threshold based on a
local histogram analysis)
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Segmentation: Point-oriented Procedures
• Definition of optimal thresholds by adaptation of probabiliy
density distributions to the histogramm
• Incorporation of model assumptions
• Example: Assumption: three structures are searched for.
Intensity values are normally distributed.
• Approach:
• 1. Estimation of parameters of the normal distribution (mean,
standard deviation) based on the histogram.
• 2. Estimation of thresholds to minimize the segmentation error.
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Segmentation: Point-oriented Procedures
Example: Threshold definition for the segmentation of brain
structures in MRI (From: [Hahn, 2001]).
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Segmentation: Point-oriented Procedures
Adaptation of 3
Gaussian
distributions to the
histogram of an MRI
brain dataset.
Criterion: Minimal
quadratic error
between histogram
and model function
(Least Square Fit).
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Segmentation: Point-oriented Procedures
• Intensity-based segmentation and
definition of regions (connected
component analysis, CCA)
• Application: segmentation of the
kidney from CT data
© Pommert [2004]
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Segmentation: Point-oriented Procedures
Another example: Bone
segmentation by
combining thresholding
(above) and CCA (below)
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Segmentation: Region-oriented Procedures
Frequent Approaches:
• Threshold-based region growing based on seed points
(Region Growing, Volume Growing)
• Watershed transform
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Segmentation: Region Growing
• Starting from a seed pixel (white), adjacent pixels with similar
intensity are looked for
• Problem: Holes in the contour
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Segmentation: Region Growing
Region growing with interactive threshold selection.
Threshold-volume diagram supports the threshold detection.
Strong discontinuities in the diagram are “candidates” for
thresholds.
(From: Boskamp et al. [2004])
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Segmentation: Region Growing
Problem: Leakage
Refinement:
Masking of “disturbing” regions
(pre-masking) by setting marks.
(From: Boskamp et al. [2004])
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Segmentation: Region Growing
Pre-maskings for a
subsequent region growing.
The target structure (left) is
separated from the
disturbing structure (right).
Source: Boskamp et al. [2004]
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Segmentation: Region Growing
Results of vessel segmentation
→ Video: Hepatic_Vasculature_1,
Hepatic_Vasculature_2
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Segmentation: Region Growing
Results of vessel segmentation
→ Video VesselSeg3D Movie
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Segmentation: Region Growing
• Advanced approaches:
• User specifies a direction for the growing process.
• Thresholds are adapted to the local intensity distribution.
• Consideration of gradient strength. Adding voxels terminates at
voxels with high gradient magnitude.
• Combination with knowledge representation.
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Segmentation: Region Growing
Combination with knowledge representation.
Fitting cross sections of an ellipse to avoid leakage.
Segmentation of the coronary artery.
Source: Hennemuth et al. [2005]
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Segmentation: Region Growing
Result of the modified region growing segmentation
(From: Hennemuth et al. [2005])
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Segmentation: Watershed Transform
• Idea: Consider the gradient image as mountains that are
flooded. Associated catchment basins correspond with
one object.
• Gray values as elevations; water creates a catchment
basin around local minima. Watersheds are created
between the catchment basins.
• Each catchment basin is assigned a representative value
(mean value) –> creation of a mosaic picture.
• Smaller (lower) basins are merged via “flooding”.
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Segmentation: Watershed Transform
Source: Hahn et al. [2000]
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Segmentation: Watershed Transform
Example
• Starting point: strong oversegmentation (due to noise in CT
data)
• stepwise region merging via
“flooding”
• image as hierarchy of
regions (Schindewolf et al.
[2000])
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Segmentation: Watershed Transform
Region Merging (Merge Tree)
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Segmentation: Watershed Transform
• Exclusion of sub-areas through “exclude” (creation of a new
watershed)
• Inclusion of sub-areas through “include” (removal of a watershed)
Source: Hahn et al. [2004]
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Segmentation: Watershed Transform
Segmentation of brain and ventricles
Source: Hahn et al. [2000]
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Segmentation: Watershed Transform
Source: Hahn et al. (2003)
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Segmentation: LiveWire
• Edge-based procedure is based on a path search (Dijkstra‘s
algorithm, http://www.youtube.com/watch?v=87_1K2GQFdU)
• Searching of paths with minimum costs
• Choose the cost function for the path from p to q such that the
edge represents the object boundary
• Elements of the function:
• expected gray values of the target object fz
• expected gradient strength fg
• edge direction or changes of the direction fD
• Optionally: values of the second order derivative
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Segmentation: LiveWire
• Example for a
cost graph
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Segmentation: LiveWire
• Suitability of a cost function is illustrated in the cost image (dark
means low costs)
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Segmentation: LiveWire
LiveWire segmentation of the liver.
Will be shown in the exercise!
Source: Schenk et al. (2003)
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Segmentation: LiveWire
Summary:
LiveWire is an effective approach
• if the target structure is clearly delineated,
• if the properties of the target structure and its boundary are
rather homogenous, and
• If the target structure does not exhibit many identations, such as
brain folds.
LiveWire is an intuitive method which is controlled precisely and
easily.
Organ segmentation in CT is an example where it works well, the
segmentation of brain structures in MRI is an example where it is
not appropriate.
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Segmentation: Model-based Approaches
• Idea: Problem-specific know-how is incorporated as constraint
• Examples:
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Number of objects (brain: gray and white substance, brain ventricle)
Rough size of regions
Intensity values and gradient strength
Location of objects (in relation to other (presegmented) objects)
• Parallel: voice recognition, separation of words
• Knowledge about possible words (dictionaries and combinations
of words are used)
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Segmentation: Model-based Approaches
• Example: atlas-based brain segmentation
• Approach:
• The brain of a patient is mapped to a segmented (normal) brain
• Segmentation of anatomical structures is adopted
• Pathological changes are structures that can not be assigned
(e.g. lesions in MS patients)
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Segmentation: Model-based Approaches
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Segmentation
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Masses are sensors that analyze the image intensity and gradient
strength
For stability: Constraints for angles, springs with high stiffness
Configuration of masses and springs represents the expected form
Stable mass-spring models for segmentation of lymph nodes (-> video),
vessels, thyroid cartilage and M. sternoclaidomastoideus
J. Dornheim et al., Proc. of MICCAI 2006 and Journal of Academic Radiology 2007
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Segmentation: Model-based Approaches
→ Video: Lymph node segmentation
→ Video: Complete lymph node segmentation
→ Video: Thyroid cartilage adjustment
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Segmentation: Model-based Approaches
Segmentation of blood vessels of the neck
J. Dornheim et al., Proc. of EG Workshop on VCBM
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→ Video: NeckVesselSegmentation
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Segmentation: Interaction
• Fully automatic segmentation is rarely performed
→ manual input before/after application of a segmentation
procedure
Forms of interaction:
• Correction of thresholds
• Limitation of the segmentation to one region of interest (ROI)
• Line drawings
• Stepwise refinement (include, exclude)
Postprocessing may be required!
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3D Object Manipulation
• Automatic model-based segmentation often causes partly
incorrect results
• Incremental and intuitive manipulation of the corresponding 3D
objects
• Inspiration: - general 3D object
- manipulation techniques
for bulging and bending of
3D objects (Igarashi‘s Teddy
system, Laplacian Modelling)
(Bending Tool, Master thesis, D. Proksch
[2009], BVM [2010])
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3D Object Manipulation
Bulging Tool
Sketch Tool
(Master thesis, D. Proksch [2009], Proksch et al. BVM [2010])
→ Videos: BendingTool, BulgeTool, SketchTool, TractionTool
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3D Object Manipulation
Further improvements:
• Model information shall be used during the correction
→
• According to the model the contour is attracted by strong
gradients and other characteristics
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Segmentation: Representation of Results
Result:
• Assignment of voxels to 1 or more objects
• Objects may:
• overlap
• be hierarchically structured (lung tumor)
Representation:
• 1 bit per object
• Segmentation image (1 bit combination per voxel that specifies to
which objects the voxel belongs)
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Overlapping Structures
• Tumor voxels are also voxels of the liver
parenchyma
• Infiltrations
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Overlapping Structures
• Problem:
no explicit voxel assignment any longer
• 1st solution:
• Explicit assignment of each structure to 1 bit of
an 8 byte value
• Limited to 64 structures
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Multicoded Segmentation Masks
Refined solution:
• Serial creation of a new volume by adding a segmentation mask
• Storage of voxel values in a Lookup table
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Multicoded Segmentation Masks
Small example.
Classification of voxels to 4 objects. Reduction of theoretically 16
possibilities to 7 (reduction of 4 bit to 3).
The reduction effect is larger for (realistically) larger examples.
(Source: Mühler et al., 2010)
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Multicoded Segmentation Masks
Advantages:
• Only 1 volume left
• According to the number of overlappings "many"
structures are storable in 1 data set
• Table: 1-3 bytes required
HLA = neck dissection
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Visualization of Segmentation Results
• Standard approach: use of a binary mask
(0 background, 1 object)
• Visualization via Marching Cubes with threshold value 0.5
• Problem: Quality, especially in case of large slice distances
• Possible solutions: Interpolation of inter layers (e.g. Cubic
Interpolation); high storage requirements
• Instead of Marching Cubes: Cubic Interpolation
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Visualization of Segmentation Results
Arteria carotis. Slice distance: 4 mm. Middle: cubic interpolation of inter
layers, right: shape-based interpolation. After interpolation: isotropic data.
(Images: Tobias Mönch, Vis. group)
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Visualization of Segmentation Results
Visualization of segmentation results as contours.
Quelle: Zachow [2004]
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Visualization of Segmentation Results
Brain vessels extracted from MRI data. “Normal” and enhanced
interpolation. Transfer functions not fully identical. Thus, details
are missing (right).
Screenshot: Fernando Vega,
Universität Erlangen
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Visualization of Segmentation Results
• Surface relaxation. Small deformation, which smoothes and
minimizes the surface. The binary volume defines constraints (this
minimizes the error).
Eye with optic nerve. Source: Insight Toolkit
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Visualization of Segmentation Results
Left: Marching Cubes
Right: Reduction of aliasing
artifacts
Brain illustration
Source: Insight Toolkit
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Morphological Operators: Erosion
Processing of ultrasound data with erosion,
[Sakas, 1995]
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Morphological Operators: Erosion
Advanced morphological processing to close holes in a bone
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Skeletonization and Analysis of Image Data
• Skeleton: form-describing structure
• Discrete skeleton: 1 voxel-wide line that proceeds through the
middle of the object.
• Motivation:
• Basis for measurement (e.g. vessel radii)
• Basis for analyzing branchings
• Path planning for virtual endoscopy (VL)
• Basis for vessel visualization (VL 9)
• Skeletonization:
• Centers of maximum circular disks
• Continued erosion (thinning)
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Skeletoinzation: Illustration
• Connection of the centers of maximum circular disks
• Grass fire: the outer areas, which remain after burning down the
grass fire, form the skeleton
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Skeletoinzation: Approaches
• Thinning: gradual erosion of the skeletonized object until a 1
voxel-wide line results.
• Search for centers of maximum circular disks
• Approach:
• Distance transformation calculation for all object points
• Determination of the centers of maximum circular disks
• Connection of the located centers
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Skeletoinzation: Problems
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Irrelevant side branches (b)
Lines that are 2 pixels wide (c)
Topology is not preserved after rotation!
Many procedures are not (hardly) transferable to 3d
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Filtering of Irrelevant Side Branches
• Criteria:
• Absolute length of the side
branches
• Ratio: length side branch/main
branch
• Hierarchy position (only lowest
level branches can be
irrelevant)
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Quantitative Analysis of Medical Image Data
Why is a quantitative analysis carried out?
• In addition to a visual review
• Objektivization of diagnoses and courses of disease
• Decision support for continuation/termination of a therapy
(chemo, hormone, drug therapy)
• Therapy planning (security edges)
• Geometrical modeling of implants
• Visualization of the quantitative analysis (e.g. bone density)
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Quantitative Analysis of Medical Image Data
What is analyzed?
• Number, dimension and volume of pathological structures
(tumors, infarct areas, herds in MS patients)
• Angle between anatomical structures (e.g. to assess
malpositions)
• Distance between pathological structures and land marks
(description of localization)
• Distance between pathological structures and organs at risk (for
therapy planning)
• Gray values of objects (mean value, deviation)
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Quantitative Analysis: Volumetry
• Volumetry of compact objects: Segmentation and subsequent
multiplication of voxel number and voxel size
• Problem: processing of boundary voxels, especially in case of
filigree structures with many edge voxels (partial volume effect)
• Goal: Classification to objects on a sub-voxel level
(Voxel vi: 10 % Obj1, 90 % Obj2)
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Quantitative Analysis: Volumetry
• Histogram-based analysis of the partial volume effect. If
there is a “high” plateau between maxima in the histogram
(intensity values that cannot be clearly assigned to a
structure), the volumetric uncertainty is huge.
• Example: Volumetry of
brain ventricles
(Schindewolf et al. [1999])
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Quantitative Analysis: Measurement of the Extent
• Goal:
Identification of the prolongation of an object o
• First idea: Identification of the axis-oriented Bounding Box
• Approach: Search through all coordinates and identify
minima and maxima in x, y and z direction.
• Problem: The calculated prolongation changes as soon as
the object is rotated.
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Quantitative Analysis: Measurement of the Extent
• Goal:
Identification of the maximum diameter of an object o
• Idea:
Application of a main axis transformation
• Approach: Identification of the barycenter and the main axes
(mechanical interpretation: axes of inertia) that characterize the
orientation of o.
• Result:
Local, rectangular coordinate system with barycenter
as origin and length of the diameter in these new
axes (Oriented Bounding Box).
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Quantitative Analysis: Measurement of the Extent
1. Identification of the barycenter vector m
2. Subtraction of the barycenter:  pi from P: pĩ = pi – m
3. Identification of covariance matrix A:
1  (pĩx)2
 ((pĩx) (pĩy))
A = –  ((pĩx) (pĩy))  (pĩy)2
N  ((pĩx) (pĩz))  ((pĩy) (pĩz))
 ((pĩx) (pĩz)
 ((pĩy) (pĩz))
 (pĩz)2
4. Identification of the Jacobian matrix C, such that A = C-1AC
(these are the normalized eigenvectors of covariance matrix A)
5. Virtual object rotation according to matrix C
6. Calculation of the Bounding Box of the rotated object (OBB) to
define the length of the main axes
7. Back-transformation according to C-1 through transposition
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Quantitative Analysis: Measurement of the Extent
Calculation principle
Example of use (3d)
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Quantitative Analysis: Distance Transform
• Goal: Emanating from a structure (feature points), all pixels
shall be assigned the integral distance to this structure.
• Result: Distance Map (Source: Lohmann [1998])
• Applications:
• Assessment: Which structures are located within a certain
edge and another structure?
• Question to determine influence areas (e.g. of vessels): Is
a voxel closer to structure1 than to structure2?
• Metrices
• Euclidean Metrics: DE [(i,j), (h,k)] = sqrt ((i-h)2 + (j-k)2)
• City-Block Distance: D4 [(i,j), (h,k)] = |i-h| + |j-k|
• Chessboard metrics: D8 [(i,j),(h,k)] = max{|i-h|, |j-k|}
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Quantitative Analysis: Distance Transform
Identification of
the supply areas
of blood vessels
MevisLab
EuclideanDTF
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Implementation of Image Processing Algorithms
Concepts for efficient image processing:
• Division of an image page by page or tile by tile
• Processing only after request of a display (Lazy Evaluation)
• Caching strategies
• Processing of single tiles/pages in separate threads
(all such concepts are supported in MeVisLab; to some extent, the
usage requires dedicated programming, e.g. in case of threads)
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Summary
• Numerous segmentation methods are necessary to cope with the
variety of biological structures and imaging procedures
• Generally applicable vs. special procedures
• Segmentation often as core of a pipeline with preprocessing of the
images and postprocessing of the segmentation results
• Skeletonization is an image analysis step that is based on
segmentation
• Often, the quantitative analysis is a decisive advantage of digital
image analysis
Application: Specification of diagnoses and courses of disease.
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Literature
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Literature
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