vision, video and virtual reality feature extraction lecture 9 image segmentation csc 59866cd fall...
Post on 21-Dec-2015
232 Views
Preview:
TRANSCRIPT
Vision, Video
and Virtual Reality Feature ExtractionFeature Extraction
Lecture 9
Image Segmentation
CSC 59866CDFall 2004
Zhigang Zhu, NAC 8/203Ahttp://www-cs.engr.ccny.cuny.edu/~zhu/
Capstone2004/Capstone_Sequence2004.html
Vision, Video
and Virtual Reality Finding CirclesFinding Circles
If we don’t know r, accumulator array is 3-dimensional If edge directions are known, computational complexity if reduced
Suppose there is a known error limit on the edge direction (say +/- 10o) - how does this affect the search?
Hough can be extended in many ways….see, for example: Ballard, D. H. Generalizing the Hough Transform to Detect Arbitrary Shapes, Pattern
Recognition 13:111-122, 1981. Illingworth, J. and J. Kittler, Survey of the Hough Transform, Computer Vision,
Graphics, and Image Processing, 44(1):87-116, 1988
Vision, Video
and Virtual Reality Region SegmentationRegion Segmentation
Partitioning of an image into different regions (connected components), each having uniform properties in some (set of) image feature(s): gray value color value(s) textural qualities local gradient motion shape info ..... etc.
Vision, Video
and Virtual Reality Goal of SegmentationGoal of Segmentation
Segment a scene into image elements which may correspond to meaningful scene elements
High Level Interpretations
Objects
Scene Elements
Image Elements
Raw Images
Vision, Video
and Virtual Reality Primary Goal of SegmentationPrimary Goal of Segmentation
“Segmenting an image into image elements which may correspond to meaningful scene elements”
What sort of image elements may correspond to meaningful scene elements?
Answer depends on type and complexity of images: Less constrained scenes must be segmented more conservatively.
Segmentation is not a well defined problem.
Vision, Video
and Virtual Reality Color Image SegmentationColor Image Segmentation
Given a grayscale image, how do we generate a region segmentation? In general, regions can be formed from the original image data or from
'derived' images: - color images from R, G, B - textural images - displacement images from motion analyses - 3D depth images
?
Vision, Video
and Virtual Reality Problems with SegmentationProblems with Segmentation
In general, high level contextual knowledge is required for successful segmentation
Vision, Video
and Virtual Reality Formal Definition of RegionsFormal Definition of Regions
A region segmentation of an image, I, is a partition of the set of pixels of I into a set of K regions {Rj}, 1≤j≤K, such that:
1. I =”
i=1
K
Rj
2. Ri Rj = for i ≠ j
3. p connected to p’ for all p, p’ in Rj
4. For some predicate P
P(Ri) is TRUE for I = 1,2,…,KP(Ri Rj) is FALSE for Ri, Rj adjacent and i≠j
Every pixel belongs to a regionEvery pixel belongs to a region
No pixel belongs to more than one regionNo pixel belongs to more than one region
Spatial coherenceSpatial coherence
Feature coherenceFeature coherence
Vision, Video
and Virtual Reality Representing RegionsRepresenting Regions
Region Occupancy Map A set of region labels in registration with image I
specifying the region association for each pixel
1 1 1 1 1
1 1 1 1 1
1 1 1
1 1
1 1 1
1
2 2 2 2 2
2 2 2 2 2
2 2 2 2 2
2 2 2 2 2
2 2 2 2
22 2
2
3 3 3
3 3 3
4
4
4
4
4
4
4
4
4
4
4
4
5 5 5
5 5 55
5 5 555
5 5 555
5 5 555
5 5 555
55
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
7 7 7 7 7 7
77
7 7 7 7
7 7 7 7 7 7
1
8 8 8 8 8
8 8 8 8 8
8 8
Image Occupancy Map or Label Plane
Vision, Video
and Virtual Reality Contour RepresentationContour Representation
C 12C 3C
4C
5C
6C7C
8C
9C
10C
11C 12C
13C
14C
15C16C
17C18C
R 1
2R
3R
4R
5R
6R7R 8R
20C 19C
2C 3C
4C
5C
6C7C
8C
9C
10C
11C 12C
13C
14C
15C16C
17C18C
2R
3R
4R
5R
6R7R 8R
20C 19C
1C
1R
R1 : {C
1,C
8,C
11}
R8 : {C
1,C
5,C
17}
.
.
.
Image
Vision, Video
and Virtual Reality Chain CodeChain Code
The chain code representation of a boundary is found by 'walking' counterclockwise around the boundary and recording the direction to turn to stay on the border:
3 2 1 4 0 5 6 7
Direction Code
Vision, Video
and Virtual Reality Chain CodeChain Code
3 2 1 4 0 5 6 7
CC = (i,j) {5 5 6 6 6 0 0 0 0 0 0 0 1 1 2 2 2 4 4 5 4 3 4 4}
Vision, Video
and Virtual Reality Region SegmentationRegion Segmentation
Basic Approaches Generalized thresholding Region growing Region merging Region splitting Split and Merge Extensions to split and merge K-means clustering Watershed algorithms
Partitioning methods Grouping methods
Vision, Video
and Virtual Reality Partitioning MethodsPartitioning Methods
Partitioning: Given: a large data set. Goal: carve it up according to some notion of the association between items inside the set. We would like to decompose it into pieces that are “good” according to our model. For example, we might:
decompose an image into regions which have coherent color and/or texture inside them; take a video sequence and decompose it into shots — segments of video showing about the same
stuff from about the same view point; decompose a video sequence into motion blobs, consisting of regions thatwhave coherent color,
texture and motion.
Vision, Video
and Virtual Reality Grouping MethodsGrouping Methods
Grouping: Given: a set of distinct data items Goal: we wish to collect together sets of data items that “look similar” according to our
model. Effects like occlusion mean that image components that belong to the same object are often
separated. Examples of grouping include:
collecting together tokens that, taken together, form an interesting object collecting together tokens that seem to be moving together. Collecting together regions that have similar color and/or texture
Vision, Video
and Virtual Reality Region SegmentationRegion Segmentation
Two Basic Techniques Region Merging
START with many trivial regions (each pixel?) MERGE regions into larger regions based on some similarity criteria CONTINUE merging until no further merging is possible
Region Splitting START with a single large region (entire image?) SPLIT into several smaller regions based on a 'splitting' criterion CONTINUE until no further splitting is possible (regions are 'uniform')
Vision, Video
and Virtual Reality Region SegmentationRegion Segmentation
Basic Approaches Generalized thresholding Region growing Region merging Region splitting Split and Merge Extensions to split and merge K-means clustering Watershed algorithms
Vision, Video
and Virtual Reality Generalized ThresholdingGeneralized Thresholding
RLP(i,j) = k if Tk-1 <= I(i,h) < Tk k = 1,...,m Tk are thresholds. m is the number of distinct thresholds. RLP (Region Label Plane) may contain significantly more than m 'regions', hence connected components must be found and the
regions relabeled with distinct label numbers. The thresholds Tk may depend on:
the entire image I(i,j), GLOBAL THRESHOLDS N(i,j) (local neighborhood), LOCAL THRESHOLDS or I(i,j) and N(i,j). DYNAMIC THRESHOLDS
To apply thresholding, must determine: m - the number of thresholds, and, Tk - the threshold values.
Vision, Video
and Virtual Reality Threshold SelectionThreshold Selection
Manual: try one and see if it looks good Histogram analysis
Strategies Search for minimum between P1 and P2
(search for minima between several peaks - multi-thresholding) Fit second order equation
Differentiate to find minimum Smooth image and/or histogram first Histogram only points not on edges in histogram
Or unweight contribution of pixels having high gradient magnitude Gray level g
p(g)
Threshold T
P1
P2
Vision, Video
and Virtual Reality Threshold SelectionThreshold Selection
Gaussian fitting Intensity distribution for objects assumed to be normally distributed Minimize false positives/false negatives
Match properties of binary and gray level image e.g. moments
Choose threshold to maximize/minimize some function of the total edge gradient Maximize property of image or histogram
e.g. entropy
…………and probably lots of others
Vision, Video
and Virtual Reality Optimal ThresholdingOptimal Thresholding
Approximate the histogram using a weighted sum of two or more probability densities with normal distribution Threshold set at the closest gray level corresponding to the minimum probability between the maxima of two or more normal
distributions. Results in minimum error segmentation
Need to estimate parameters of the density functions Implies optimization
Probability distributions of backgrounds and object
Corresponding histograms and optimal thresholds
Vision, Video
and Virtual Reality Local or Adaptive ThresholdingLocal or Adaptive Thresholding
Intensity values can vary as a function of lighting (for example)….e.g.:
Very difficult to threshold using conventional methods.
Vision, Video
and Virtual Reality Local or Adaptive ThresholdingLocal or Adaptive Thresholding
Each pixel in image needs a unique threshold Two basic approaches
Chow and Kaneka Adaptive Thresholding (1972) Compute thresholds in a local window at sampled locations using histogram
technique Interpolate local thresholds across image
Local Thresholding Examine statistically pixel values in local neighborhood around pixel to be
thresholding Use local statistic as threshold Possibilities include mean, median, or mean of max and min value
Mean of 7x7 neighborhood
Vision, Video
and Virtual Reality Improved ResultsImproved Results
Results can be improved if the threshold employed is not the mean, but (mean-C), where C is a constant.
Using this statistic, all pixels which exist in a uniform neighborhood (e.g. along the margins) are set to background.
Mean7x7 neighborhood; C=7
Mean75x75 neighborhood; C=10
Median7x7 neighborhood; C=4
Vision, Video
and Virtual Reality Region SegmentationRegion Segmentation
Basic Approaches Generalized thresholding Region growing Region merging Region splitting Split and Merge Extensions to split and merge K-means clustering Watershed algorithms
Vision, Video
and Virtual Reality Region GrowingRegion Growing
Goal: Segment the image my repeatedly starting from a particular pixel, called a "seed" point, growing it into a region by iteratively adding neighboring points while some similarity criterion is met.
Is a set of algorithms to group pixels with similar attributes together GENERAL IDEA
A pixel is added to a partially grown region if two conditions are satisfied: The pixel must be adjacent to the region, and, The pixel must be "similar enough" to pixels already in the region.
The process continues until no further points can be added. Some other seed point, not already in any region, is chosen and the process is repeated until the entire image is
segmented.
Vision, Video
and Virtual Reality Region GrowingRegion Growing
Use a region label plane RLP same size as the original image contains a 1 if the corresponding image point is in the
region, 0 otherwise initially contains a 1 corresponding to the seed point
32 15 13 11 12 10 13 9
12 12 11 11 13 11 8 10
15 13 10 10 12 14 16 9
14 12 18 17 11 14 20 19
13 11 16 17 9 11 18 17
13 11 16 17 9 11 17 19
12 10 18 16 10 11 16 20
15 12 17 19 11 10 18 22
1
Image Region Label Plane
Vision, Video
and Virtual Reality Similarity CriteriaSimilarity Criteria
When is a pixel "similar enough" to be added to the region? different choices:
statistical population tests simple feature differences
General Idea Apply iteratively to all pixels until no more pixels are added.
IF RLP(i,j) = 0AND RLP(i-n, j-m) = 1 for some n,m = -1 to 1AND |I(i-n, j-m) - I(i,j)| < T (a predefined threshold)
THEN RMP(i,j) = 1
Vision, Video
and Virtual Reality Example: Simple Region GrowingExample: Simple Region Growing
Seed Point
T=16 T=32
T=64 T=128
Vision, Video
and Virtual Reality ProblemsProblems
What’s the similarity criterion? How do I select the threshold? Why does the algorithm ‘leak’?
Because of leaks, features in a region can vary arbitrarily. Fixed thresholds do not take into account characteristics of global spatial distribution.
pixel sequence: p1,..., pk
pj, pj+1neighbors| pj - pj+1| < T but | p1 - pk| > T
p1
pk
Vision, Video
and Virtual Reality Region SegmentationRegion Segmentation
Basic Approaches Generalized thresholding Region growing Region merging Region splitting Split and Merge Extensions to split and merge K-means clustering Watershed algorithms
Vision, Video
and Virtual Reality Region MergingRegion Merging
Define a distance function between regions. general form:
dij = D(Ri, Rj) > 0
Typically D is a distance measure in feature space and is a function only of the feature vectors associated with regions Ri and Rj:
dij = D(fi, fj) > 0
Merge regions with minimum distance Need to define some kind of termination criteria
Vision, Video
and Virtual Reality Example Distance MeasuresExample Distance Measures
Distance between color means
Distance between region centers
Weighted combination of the two
Where Nm is the number of pixels in Rm
cij =Ni
Nnew
Nj
Nnew|i - new|
2|j - new|
2+
rij =Ni
Nnew
Nj
Nnew|ri - rnew|
2|rj - rnew|
2+
dij = cij + rij
Vision, Video
and Virtual Reality Region MergingRegion Merging
Define a distance measure dij = D(f(Ri), f(Rj)) >0 Algorithm:
{ While termination condition false
Determine the minimum distance regions
{i*, j*} = arg min dij
Merge the minimum distance regions
Ri* Ri* U Rj*
Remove merged region from region list L L-{Rj*
Compute termination condition
}
i,j
Ri, Rj L
Vision, Video
and Virtual Reality Merging HierarchyMerging Hierarchy
Algorithm generates a binary tree
Merging can be terminated when the minimum distance exceeds a threshold
d i*,j* > T stop merging Different thresholds produce different segmentations
Vision, Video
and Virtual Reality Fisher’s CriterionFisher’s Criterion
Mean and variance are good features to use for merging Especially if data is distributed normally
e.g. is modeled by the Gaussian distribution Peak occurs at (the mean) and has a value a a is (1 / 22) and ensures that the area under the curve = 1
For modeling histograms Compute area under the histogram and divide by (2 ) Parameter is called the variance
= sqrt () is the standard deviation measures the ‘flatness’ of the distribution
1/2
1/2
Vision, Video
and Virtual Reality Fisher’s CriterionFisher’s Criterion
Discrimination between regions of different means and standard deviations can be done using Fischer’s criterion:
is a threshold If two regions have good separation in the means and low variance, then we can separate them.1 - 2
1 - 22
2
>
Vision, Video
and Virtual Reality UniformityUniformity
Thus, the merging threshold for the mean intensity for two adjacent regions, should vary depending on the expected uniformity of the merged region
Less uniform regions will require a lower threshold to prevent under merging Uniformity a function of both intensity mean and variance of the region
Combine them (heuristic) as Uniformity = 1 - / In range 0-1 for case where the samples are all positive
The threshold value decreases with the decrease in uniformity as = (1 - / ) 0
User need supply only one threshold 0
2
2
Vision, Video
and Virtual Reality Region SegmentationRegion Segmentation
Basic Approaches Generalized thresholding Region growing Region merging Region splitting Split and Merge Extensions to split and merge K-means clustering Watershed algorithms
Vision, Video
and Virtual Reality Region SplittingRegion Splitting
Region Splitting:(1) Start with a single large region (initially, entire image).
(2) Recursively split it into smaller regions.
(3) Continue splitting until each region is uniform (no further splits are possible).
A simple approach: Global Thresholding Define a global threshold T Apply to every pixel in the image I:
RLP(i,j) = 0 if I(i,j) < T
RLP(i,j) = 1 if I(i,j) ≥ T
Vision, Video
and Virtual Reality Region splitting: Multiple FeaturesRegion splitting: Multiple Features
Old algorithm: Ohlander-Price Basically a sequential histogram-based multiple threshold algorithm. Features used RGB, HSI, and YIQ (9 images) General Idea:
Start with the entire image as the initial region. Get the next region to be segmented
if none - the segmentation is complete. Compute the set of one-dimensional histograms. Select the "best" peak and find valleys on either side
if none, the region is "done" - put on finished list. Apply the threshold to the region and determine connected components. Add these regions to the list of regions to be further segmented and go to step 1.
Vision, Video
and Virtual Reality Peak Selection CriteriaPeak Selection Criteria0 Intensity peak in 0-60 or 200-255 ranges
Best is closest to end
1 Both minima < 10% highest value max/min ratio > 4
Another peak exists with max/min ratio > 2
2 Both minima < 25% of the peak value max/min ratio > 2
Another peak with max/min ratio > 2
3 Max/min ratio > 2 Another peak with max/min ratio > 2
If maxima are within 10%, then both are acceptable
(a bimodal distribution)
4 (Saturation only) Minima in 0-200 (lowest 20%)< 25% of the peak value
max/min ratio > 2
Specified minima must separate peak with max/min ratio > 1.2
5 Minima < 10% of highest value
10% of all points must be outside the peak
6 Minima < 70% of highest value
max/min ratio > 1.7
Vision, Video
and Virtual Reality Region SegmentationRegion Segmentation
Basic Approaches Generalized thresholding Region growing Region merging Region splitting Split and Merge Extensions to split and merge K-means clustering Watershed algorithms
Vision, Video
and Virtual Reality Hybrid TechniqueHybrid Technique
Split and Merge combination: splits followed by merges (or vice-versa) split and merge decisions can be either
local: a pixel and its immediate neighbors
a region and its immediate neighbors global: on the basis of a large number of
pixels scattered throughout the image
Vision, Video
and Virtual Reality Split and MergeSplit and Merge
General idea: Begin with an arbitrary region decomposition in a quadtree plane
Initial decomposition = entire image? Split each region which violates a uniformity predicate into its 4
quadtree children Merge (recursively) all regions which jointly satisfy a uniformity
criterion Supporting data structure: region adjacency graph
R
R1 R2 R3 R4
R41 R42 R43 R44
R1 R2
R3R41 R42
R43 R44
Vision, Video
and Virtual Reality Region SegmentationRegion Segmentation
Basic Approaches Generalized thresholding Region growing Region merging Region splitting Split and Merge Extensions to split and merge K-means clustering Watershed algorithms
Vision, Video
and Virtual RealitySegmentation by k-means clusteringSegmentation by k-means clustering
Assume we know the data has k clusters (k known) Each cluster is assumed to
have a center ci
The jth element to be cluster is described by a feature vector xj
For scattered points, x would be coordinate(s) For an intensity image, x might be the intensity at a pixel
Define an objective function that measures how good the clustering result is.
Develop an algorithm to maximize the objective function.
Vision, Video
and Virtual Reality Objective FunctionObjective Function
Assume that element are close to the center of their cluster One possible objective function is
Note that if allocation of points to clusters is known, we can compute the best center easily Far too many associations of points to clusters to search this space for a minimum Instead, define an algorithm that alternates
Assume centers are known, allocate points Assume allocation is known, compute centers
Vision, Video
and Virtual Reality k-means algorithmk-means algorithm
Choose k data points to act as cluster centers Random selection First k data points
Until the cluster centers are unchanged Allocate each data point to cluster whose center is nearest Now ensure that every cluster has at least one data point; possible techniques for doing this include:
supplying empty clusters with a point chosen at random from points far from their cluster center. Replace the cluster centers with the mean of the elements in their clusters.
end Apply connected components algorithm to generate regions
Vision, Video
and Virtual Reality ExampleExample
Assume k=5
Each pixel is represented by the mean value of the cluster to which the pixel belongs A connected components algorithm must be applied to make these true region segementations
Original Image k-means on intensity k-means on color
K=5
Vision, Video
and Virtual Reality Results, k=11Results, k=11
Sample clusters with k-means clustering based on color
Vision, Video
and Virtual Reality Other Distance MeasuresOther Distance Measures
Suppose we want to have compact regions New feature space: 5D
(2 spatial coordinates, 3 color components)
Points close in this space are close both in color and in actual proximity Problem with simple Euclidean distance:
what if coordinates range from 0-1000 but colors only range from 0-255? Depending on how things are scaled, gives different weight to different kinds of data
Weighted Euclidean distance: adjust weights to emphasize different dimensions
22)( iii yxcyx 22)( iii yxcyx
Vision, Video
and Virtual Reality Hybrid Edge-Region ApproachesHybrid Edge-Region Approaches
Same idea as region merging—start with oversegmented image. Use edge detection information as well. Merge not based on region statistics but on weak boundaries. Usually use fraction of edge pixels along shared boundary that are
below some threshold. Often used as post-processing for edge-based segmentation.
Vision, Video
and Virtual Reality Region SegmentationRegion Segmentation
Basic Approaches Generalized thresholding Region growing Region merging Region splitting Split and Merge Extensions to split and merge K-means clustering Watershed algorithms
Vision, Video
and Virtual Reality Watershed AlgorithmsWatershed Algorithms
A gray scale image can be viewed as a topographic relief map where the intensity function of the image represents the altitude.
A watershed region or catchment basin is defined as the region over which all points flow “downhill” to a common point. Points at which water would be equally likely to fall to more than one such minimum: watersheds or watershed lines Watersheds of gradient magnitude make useful region-based segmentation primitives. Boundaries of watersheds are one way to define ridges—
this is basically the
same idea as finding
a ridge of gradient
magnitude.
Vision, Video
and Virtual Reality Immersion AlgorithmImmersion Algorithm
Start with all pixels with the lowest possible value (grad. mag.) these form the basis for initial watersheds
For each intensity level k: For each group of pixels of intensity k
If adjacent to exactly one existing region, add these pixels to that region Else if adjacent to more than one existing regions, mark as boundary Else start a new region
Can use a histogram-like structure to keep lists of all pixels with each intensity level k.
Vision, Video
and Virtual Reality Watershed ProblemsWatershed Problems
Oversegmentation watershed from markers
Computationally intensive computation intensive graph algorithm and appropriate data structures graph
Graylevel might not be the optimal choice as the local similarity measure similarity measure other local features
Statistical edge enhanced image distance transformed imagee transformed image…)
Vision, Video
and Virtual Reality Over-segmentation ProblemOver-segmentation Problem
Oversegmentation due to noise and other local irregularities of the gradient
Solution: markers (of ‘object’ locations)
Vision, Video
and Virtual Reality TobogganingTobogganing
Again work on the gradient magnitude image. Link each pixel to the smallest of its neighbors. If no smaller neighbors, become a are’ region seed’. All pixels that “flow” downhill (smallest neighbor) to
the same point form a single region.
Vision, Video
and Virtual Reality Multispectral SegmentationMultispectral Segmentation
Given N multi-spectral images:1. Independently segment each multi-spectral feature image using the localized histogram
algorithm.
2. Intersect the N segmentation to create a new, combined segmentation.
3. Merge using a region merging algorithm.
See J. Beveridge, J. Griffith, R. Kohler, A. Hanson, and E. Riseman, “Segmenting Images Using Localized Histograms and Region Merging”, IJCV 2(3), January 1989, pp. 311-347
Vision, Video
and Virtual Reality Three Color UnionThree Color Union
Note: This result was obtained by taking the union of three color segmentations obtained with a more sensitive set of parameters than those shown on the previous page and consequently has more boundaries.
Vision, Video
and Virtual Reality Final Segmentation: After MergingFinal Segmentation: After Merging
Segmentation obtained from over-segmented image on previous slide after applying a rule-based merging strategy using regions similarity, size, and connectivity.
Vision, Video
and Virtual Reality Region FeaturesRegion Features
Many features can be use to characterize a region and its properties Supports many tasks, including object recognition. Example features:
area, height, and width perimeter, bounding box, area of bounding box centroid orientation compactness moments .....etc.
Vision, Video
and Virtual Reality Region FeaturesRegion Features
Basics Perimeter Area Orientation
Rotation/translation/scale invariant Compactness = perimeter2/area Rectangularity = AreaRect/AreaObject (next slide) Euler number = #regions - #holes Convexity = AreaConvexHull/AreaObject
Vision, Video
and Virtual Reality RectangularityRectangularity
W and L are a function of Rectangularity = WxL/A Choose to get WxL minimum
Called the ‘minimum bounding rectangle’
Minimized for rectangular objects
W
L
A
Vision, Video
and Virtual Reality PerimeterPerimeter
Region plane boundary
P = number of pixels on boundary
P = number of horizontal steps + number of vertical steps + 2 x number of diagonal steps
or
Vision, Video
and Virtual Reality MomentsMoments
Centroid: center of mass
Higher order moments
Note: A = m00 ; r = m10 / m00 ; c = m01 / m00 ;
r = r I(r,c)1Ar c
c = c I(r,c)1Ar c
mpq = r c I(r,c)r c
p q
Vision, Video
and Virtual Reality Central MomentsCentral Moments
Moments around the center of mass
Note that A = u00 ; u01 = 0; u10 = 0
Higher order (2nd order and higher) moments are used heavily in oject recognition
upq = (r-r) (c-c) I(r,c)r c
p q
Vision, Video
and Virtual Reality OrientationOrientation
Let be the region orientation with respect to the r axis
Can be shown that
tan 2211
20 - 02
Vision, Video
and Virtual Reality SummarySummary Covered only basic approaches
simple region growing split, merge, and split and merge algorithms generalized thresholds …….
Many approaches to region segmentation statistical techniques: parameter estimation, mode estimation, clustering, decision theoretic methods... surface fits to the intensity surface: constant, plane, or bivariate polynomial,... relaxation: traditional, stochastic (simulated annealing) markov random fields methods context sensitive and knowledge-driven methods combinations with edge detection techniques optimization and learning methods multi-resolution
Literature is enormous
top related