Symmetric Region Growing SymRG IEEE Trans. on Image Processing, vol. 12, no. 9, pp. 10071015, 2003

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Symmetric Region Growing (SymRG)IEEE Trans. on
Image Processing, vol. 12, no. 9, pp. 1007-1015,
2003

• Shu-Yen Wan, Ph.D.
• Department of Computer Science Information
  Engineering
• Chang Gung University, Taiwan, R.O.C.
• E-mail sywan_at_mail.cgu.edu.tw
• http//viz.csie.cgu.edu.tw (163.25.101.162)

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Outline

• 3D Vasculature Analysis, Topology, and Procedure
• Region-Based Segmentation
• Symmetric Region Grow (SymRG)
• Definition
• Properties
• Experiements
• Summary

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3D Vasculature Analysis Overview

• Extract and explore the embedded geometrical
  information in large 3D (three-dimensional)
  medical images containing vascular networks to
  perform physiological studies and identify the
  abnormal.

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3D Vasculature Analysis Modules
Human liver
Rat heart
Rat liver
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Schematic of CT Imaging
Figure from Huangs PACS (1999) book
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Other Medical Scanning Mechanisms
PET Positron Emission Tomography
Ultrasound
MR Magnetic Resonance
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Orthogonal Views of 3D Images
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2D Slices Dog Lung Pad
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3D-to-2D Projections
Maximum Intensity Projection (MIP)
Z
X
Weighted-Sum Projection
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Connectivity
26-connectivity
x-x1 and y-y1 and z-z1
6-connectivity
x-xy-yz-z1
9 cubes
8 cubes
9 cubes
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Analysis Procedure
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Region-Based Segmentation

• Seeded region grow
• Given initial seeds (a1,a2,a3) seed selection
  is important
• Construct homogeneous regions (R1,R2,R3)
• Relegate remaining points to background (R4)

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Collaborative Segmentation Cavity Deletion
CVGIP2002, Aug. 25-27, 2002
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Symmetry of Region Growing

• Given a ? b
• a ? c ?
• b ? a ?
• c ? a ?
• b ? c ?
• c ? b ?

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Symmetry Issues ofTraditional Region Growing

• Inherent dependence on order of points and
  regions being examined
• Computational performance difficult to improve
  (x-, y-, z-inseparable computation)

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SymRG Definitions
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Whats ?
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Region Growing Path Set
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Symmetry of Growing Paths
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Intra-Region Substitution Theorem
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Equivalent Region Theorem

• Given a ? b
• a ? c
• b ? a
• c ? a
• b ? c
• c ? b

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Theory-Reality Bridging Corollaries
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Symmetry Propagation Theorem
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SymRG Properties

• Property 1 (intra-region substitution)
  Considering SymRG, replacement of a seed may
  yield the same segmentation result.
• Property 2 (seed invariance) Considering SymRG,
  replacement of all seeds may yield the same
  segmentation result.
• Property 3 (SymRG implementation) A SymRG
  segmentation may start with the very first point
  of the image and sequentially perform region
  growing and merging and produce the equivalent
  result as those by the traditional iterative or
  recursive region-growing procedures.

CVGIP2002, Aug. 25-27, 2002
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SymRG Process Switch
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SymRG Characteristics

• Invariant segmentation results
• relatively insensitive to initial growing points
• Results more reproducible
• Enable x-, y-, z-separable computation
• Facilitate parallel processing
• Natural to design time- and computation-efficient
  algorithms

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Example A 3D Symmetric Region Growing Algorithm

• 2D Symmetric Region Growing
• For row i 0 to Ny-1.
• Construct 1D regions (actually segments) by
  applying I and X
• If i ? 1, Do Region Merging for rows i and (i-1)
• Apply S to validate regions. Regions containing
  no seeds are relegated to the background
• 3D Symmetric Region Growing
• For slice k 0 to Nz-1.
• Perform 2D Symmetric Region Growing on slice k
• If k ? 1, Do Region Merging for slices k and
  (k-1)
• Apply S to validate regions. Regions containing
  no seeds are relegated to the background. For
  each point p, f(p) region label, if it
  belongs to a region of interest otherwise, f(p)
  0.

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SymRG 2D Equivalent Implementation

• Construction of region and equivalence tables
• Gray-scaled and binary (generic segmentation and
  connected-component labeling or CCL)
• Parallelism
• Seed-insensitive

CVGIP2002, Aug. 25-27, 2002
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SymRG Applications

• Fast and memory-efficient region growing
• Connected component labeling
• Cavity deletion
• Previous algorithms may determine whether to
  produce invariant segmentation results by
  verifying their symmetry

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Experiment Setup

• Cases studied
• A human-liver EBCT image (Humliv)
• Three rat-liver micro CT images (control1,
  control2, control3)
• Experiment platforms
• Sun machine (CPU 250MHz OS Solaris 2.5.1)
• PC (CPU 400MHz OS Windows NT 4.0)
• Implementation Details
• Programming Language C
• 3D foreground connectivity 26-connectivity

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Human Liver Image (Humliv)

• Size 48.8 MB (16-bit)
• 24.4MB (8-bit)
• Subject human liver, bile ducts
• Dimensions 302?389?218
• Voxel resolution
• ?x ?y ?z 58.6 ?m
• Contrast agent to opacify arteries
• Root in the bottom right quarter

Coronal (x-z) maximum-intensity projection (MIP)
of Humliv
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Humliv Segmentation Results
Surface rendering of segmented Humliv
Segmented Humliv image with cavities removed
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Rat Liver Image 1

• Size 73 MB (16-bit)
• 36.5MB (8-bit)
• Subject rat liver, bile ducts
• Dimensions 319?247?487
• Voxel resolution
• ?x ?y ?z 21?m
• Contrast agent to opacify arteries
• Root on the left center

Coronal (x-z) maximum-intensity projection (MIP)
of Control1
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Control1 Segmentation Results
Segmented Control1 image with cavities removed
Surface rendering of segmented Control1
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Rat Liver Image 2

• Size 80.2 MB (16-bit)
• 40.1MB (8-bit)
• Subject rat liver, bile ducts
• Dimensions 399?215?491
• Voxel resolution
• ?x ?y ?z 21?m
• Contrast agent to opacify arteries
• Root on the lower-left corner

Coronal (x-z) maximum-intensity projection (MIP)
of Control2
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Control2 Segmentation Results
Segmented Control2 image with cavities removed
Surface rendering of segmented Control2
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Rat Liver Image 3

• Size 114.4 MB (16-bit)
• 57.2MB (8-bit)
• Subject rat liver, bile ducts
• Dimensions 400?400?375
• Voxel resolution
• ?x ?y ?z 21?m
• Contrast agent to opacify arteries
• Root in the lower-left quarter

Coronal (x-z) maximum-intensity projection (MIP)
of Control3
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Control3 Segmentation Results
Segmented Control3 image with cavities removed
Surface rendering of segmented Control3
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Running Time Comparisons
(in Seconds)
The past approach is an implementation as
proposed in Higgins1996. SymRG (1) is performed
on a Sun machine that has one 250MHz CPU running
Solaris 2.5.1, while SymRG (2) on a PC that has a
400MHz CPU running Windows NT 4.0.
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Memory Usage Comparisons
(in MBs)
The past approach is an implementation as
proposed in Higgins1996. SymRG (1) retains a copy
of the image in the image to avoid I/O overhead,
while SymRG (2) keeps only six slices of the
image at a time in the memory when the memory
resource is limited.
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Summary

• Novel region-growing paradigm
• Insensitive to initial growing points (seeds)
• Save BOTH computation time and memory
• Apply to images of any dimensionality
• Computation of each dimension separable
• Study of region-growing topology
• Future Research
• Categorization of existing region-growing methods
• Optimization of region-growing criteria
• Heuristic symmetric region-growing designs for
  asymmetric methods

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Thanks for your attention!
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Challenges

• Control1
• Size 80.2 MB (16-bit)
• Subject rat liver, bile ducts
• Dimensions 399?215?491
• Voxel resolution ?x?y?z21?m

• Manual analysis far too time-consuming
• Automatic analysis requires considerable
• storage processing space
• computational complexity
• Efficient network representation is critical
• Root identification
• 3D Visualization to interact with extracted
  information

• Control2
• Size 114.4 MB (16-bit)
• Subject rat liver, bile ducts
• Dimensions 400?400?375
• Voxel resolution ?x?y?z21?m

• Control3
• Size 73 MB (16-bit)
• Subject rat liver, bile ducts
• Dimensions 319?247?487
• Voxel resolution ?x?y?z21?m

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3D Sigma Filter
Reduces image noise, sharpens regions and retains
thin lines.
N(x,y,z) is the (2w1)X(2w1)X(2w1) neighborhood
about voxel (x,y,z), w is an integer, Nc(x,y,z)
are those voxels (l,m,n) in N(x,y,z) satisfying
v(l,m,n)-v(x,y,z)lt2?, NccardNc(x,y,z), and
card(A) denotes the cardinality (or voxel count)
of set A. For our efforts, if fewer than 9 of
the voxels in N(x,y,z) are close to the voxel of
interest, then the voxel is left unchanged such
a voxel is presumably a thin-line voxel.
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3D Seeded Region Growing

• Symmetric Region-Growing Variant
• Voxel intensity and 3D connectivity used
• Two stages
• Per slice 2D region growing
• Region merging between consecutive slices
• Memory efficient - 1 copy of image needed
• Low computation - single pass for two stages

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3D Cavity Deletion

• Resolve boundary problem of Higgins et al. 1996.
• A variation of 3D seeded region growing
• computes image complement
• performs 3D 6-connected component labeling
• removes cavities (regions not touching the
  boundary)
• computes image complement again

GminGseedMinGseedMaxGmax1, Gtolerance0
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3D Thinning (Skeletonization)

• Employ algorithm of Saha et al. 1994, 1997
• Skeleton preserves the homotopy
• Using module implemented by Atilla P. Kiraly.

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Axis Description Model
CVGIP2002, Aug. 25-27, 2002
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Traditional CSA Analysis
Oblique slice with predefined size
CSA Cross-sectional Area
CVGIP2002, Aug. 25-27, 2002
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SymRG-Based CS Creation Analysis

• Against segmented image
• Perpendicular to axis
• Contour search
• Determine bounding box
• SymRG-based CCL
• Measurements
• CSA
• Surface area
• Volume
• BAP (brightness area product)
• means and variances

CVGIP2002, Aug. 25-27, 2002
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Tree Definition

• Hierarchical information of branching networks
• Compact ? replace thinned image
• Fast retrieval, many measurements
• Processing to define tree structure
• Representation scheme
• Root identification and reordering
• Pruning

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Skeleton Representation (Internal)
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Skeleton Representation - External
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Root Identification and Reordering

• User specifies approximate root location
• New root is defined as the closest end voxel

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Pruning
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Segment Generation

• Fixed length
• Minimum Absolute error
• Minimum squared error

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Measurement Calculation

• Mother-daughter and sister-sister relationships
• Branching angles
• Generation ID
• Cross-section area (CSA)
• Brightness area product (BAP)
• Average branch length and CSA within a generation
• Variation of branch lengths and CSAs
• Volume loss in bifurcations

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Results rat liver (control1)
Automatic - 15 branches

• Sigma w1, ?10, root (13, 165, 292)
• segmentation80,120,255,255, tol10, conn26,
  leastSeeds5, minSixe100

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Results rat liver (control2)
Automatic - 51 branches

• Sigma w1, ?10, root (114, 205, 274)
• segmentation180,230,255,255, tol10, conn26,
  leastSeeds5, minSixe100

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Results rat liver (control3)
Automatic - 69 branches

• Sigma w1, ?10, root(13, 165, 292)
• segmentation130,200,255,255, tol10, conn26,
  leastSeeds5, minSixe100

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Results human EBCT liver (humliv)
human EBCT liver image
Automatic - 53 branches

• Sigma w1, ?10, root (270, 238, 183)
• segmentation(80,120,255,255, tol10, conn26,
  leastSeeds5, minSixe100

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Computation Time
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Computation Time (continued)
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Disk Storage

• Generally, gzipped files bigger, no branch
  information
• Skeleton-representation file directly usable

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Excerpt of Control3s Skeleton Representation
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Lca_146 (original)
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Lca_146 (segmented)
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Lca_146 (sigma filtered)
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Lca_146 (cavities deleted)
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Lca_146 (thinned)
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Lca_146 (3D Rendered)