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Low-Resolution Contour Recognition for
Hexagonal Grid Images
Contents
Introduction
Curve Bend Function (CBF)
Steps for obtaining HCBF
Subpixel Improvement
Contour Recognition for Isolated Objects
Graph Matching for Occluded Objects
Experimental Results
Introduction
The contour of an object consist a very
small number of pixels.
Difficult to find out the contour feature.
An alternative scheme.
Hexagonal grid.
Curve Bend Function (CBF)
Critical points
Locate a proper set of critical points.
Curve bend function concept.
In this method the curve bend angles in a contour
and the convexity at each critical point are
computed.
Curve Bend Function (CBF) Contd..
Pixels on a contour are represented by an array
Ω= { Si = (xi,yi), i = 0,1,…, Nt - 1},
where Nt is the total number of pixel points
Now, let J=αNt, where J is an integer
called the supported length and α is the
supported rate, 0.01≤ α≤ 0.05
The CBF of a point Si on Ω is defined as:
),()( J
iii cosrS β=g
Curve Bend Function (CBF) Contd..
The angle β is called the curve bend
angle (CBA) at Si.
si-J
si+J
si
β i
J
C i
ρ(S i,C i)
The explanation of the CBF.
Steps for obtaining HCBF
Contour of low-
resolution
hexagonal image
Hexagonal-grid curve bend function (HCBF)
Traditional
rectangular grid
Image 0 2 0 4 0 6 0 8 0 1 0 0
C o n t o u r p ix e ls
- 1 .0
- 0 .5
0 .0
0 .5
1 .0
CBFG(S)
l o w - r e s o l u t i o n s u b p i x e l h i g h - r e s o l u t i o n
Steps in generating the HCBF
A Subpixel Improvement
 The improvement achieved by the hexagonal grid is not enough.
 Subpixel Improvement is needed.
 The simple scheme used is based on the property of the SHF and
the interpolation of the intensities of neighboring pixels.
0 2 0 4 0 6 0 8 0 1 0 0
C o n t o u r p ix e ls
- 1 .0
- 0 .5
0 .0
0 .5
1 .0
CBFG(S)
l o w - r e s o l u t i o n s u b p i x e l h i g h - r e s o l u t i o n
The subpixel HCBF
values are very close
to the original high-
resolution values.
Contour Recognition for Isolated Objects
Feature Vector Matching
First identify the important features of the
contour.
Features are combined into a feature vector
Characteristics of the contour.
Type A critical points having smaller hexagonal
CBA angles,
Type B critical points are those with larger CBA
angles.
Threshold value, ψ = 120°
Feature Vector Matching
The feature vector is a six-digit numeral.
First 2 digits are Type A critical points with positive and
negative signs.
Digits 3 and 4 are Type B critical points with positive and
negative signs.
Finally, digits 5 and 6 are of convex arcs and concave
arcs, respectively.
Similarity Matching
 Similarity matching is to match two HCBF curves by directly
measuring the differences between them.
Similarity ratio,
t
t
N
S
=Φ
Data Window
The HCBF of the
sample
The HCBF of the model
The diagram of the similarity matching method
Graph Matching for Occluded Objects
The integrated method is used to find the
corresponding pairs between the model graph and
scene graph.
Select Feature points
Graph Matching
The matching results are to be interpreted
corresponding to different occurrences of every
object model in the scene.
Experimental Results
Isolated Objects
Feature vector
Similarity ratio
Model Sample
Rectangular grid 324000 322000 86%
Hexagonal grid 322000 324000 91%
Hexagonal grid with
subpixel technique
322010 322010 100%
Due to the fact that the feature vectors of the model and the sample are not the
same for rectangular grid and hexagonal grid without subpixel technique, the results
of these feature vector matching are erroneous.
Pixel
Matching schemes
Experimental Results
 The cross-matching recognition is defined for arbitrarily two different
objects that one object is a model and the other is a sample and vice
versa.
Fig: The shapes, the subpixel HCBFs and their corresponding feature codes of the patterns
Experimental Results
The similarity ratio Φ between models and samples
It’s clearly seen that, object
#1 is identical to #3 and #6,
and is similar to #2, #4 and
#9,
but object #9 is similar to
objects #1, #3, #5, #6, #8
and #12.
Experimental Results
Occluded Objects
The model graphs and their extracted feature
points in a low-resolution images
The scene graphs and their extracted feature points in
a low-resolution images
Experimental Results
Scene Resolution
feature
point
Model
matched
point
Pose (r, θ, tx, ty)
Fig. 6.10(a) 42 x 62 16 Fig. 6.9(b) 9 1.01, 0.8, -1.2, 8.0
Fig. 6.9(e) 4 0.98, -33.4, -17.9, -12.6
Fig. 6.10(b) 55 x 58 17 Fig. 6.9(c) 5 1.04, -68.4, 44.0, 9.4
Fig. 6.9(e) 4 0.98, -33.4, -17.9, -12.6
Fig. 6.9(e) 5 1.05, -68.5, 4.4, 9.4
Fig. 6.10(c) 44 x 44 28 Fig. 6.9(a) 12 1.03, -61.2, -7.3, 9.9
Fig. 6.9(a) 12 1.05, 143.9, 0.3, 4.5
Fig. 6.10(d) 39 x 52 24 Fig. 6.9(d) 8 1.06, 60.4, -2.3, 0.5
Fig. 6.9(d) 6 0.85, -31.9, 3.0, 9.1
Fig. 6.9(d) 6 0.90, 170.8, -2.0, -8.9
The matching results of the proposed method on the low-
resolution images
From the table, it can be seen that multiple occurrences of the same object in
one scene can be found simultaneously as well as their different poses.
Thank You . .

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Low-Resolution Contour Recognition for Hexagonal Grid Images

  • 1. Low-Resolution Contour Recognition for Hexagonal Grid Images Contents Introduction Curve Bend Function (CBF) Steps for obtaining HCBF Subpixel Improvement Contour Recognition for Isolated Objects Graph Matching for Occluded Objects Experimental Results
  • 2. Introduction The contour of an object consist a very small number of pixels. Difficult to find out the contour feature. An alternative scheme. Hexagonal grid.
  • 3. Curve Bend Function (CBF) Critical points Locate a proper set of critical points. Curve bend function concept. In this method the curve bend angles in a contour and the convexity at each critical point are computed.
  • 4. Curve Bend Function (CBF) Contd.. Pixels on a contour are represented by an array Ω= { Si = (xi,yi), i = 0,1,…, Nt - 1}, where Nt is the total number of pixel points Now, let J=αNt, where J is an integer called the supported length and α is the supported rate, 0.01≤ α≤ 0.05 The CBF of a point Si on Ω is defined as: ),()( J iii cosrS β=g
  • 5. Curve Bend Function (CBF) Contd.. The angle β is called the curve bend angle (CBA) at Si. si-J si+J si β i J C i ρ(S i,C i) The explanation of the CBF.
  • 6. Steps for obtaining HCBF Contour of low- resolution hexagonal image Hexagonal-grid curve bend function (HCBF) Traditional rectangular grid Image 0 2 0 4 0 6 0 8 0 1 0 0 C o n t o u r p ix e ls - 1 .0 - 0 .5 0 .0 0 .5 1 .0 CBFG(S) l o w - r e s o l u t i o n s u b p i x e l h i g h - r e s o l u t i o n Steps in generating the HCBF
  • 7. A Subpixel Improvement  The improvement achieved by the hexagonal grid is not enough.  Subpixel Improvement is needed.  The simple scheme used is based on the property of the SHF and the interpolation of the intensities of neighboring pixels. 0 2 0 4 0 6 0 8 0 1 0 0 C o n t o u r p ix e ls - 1 .0 - 0 .5 0 .0 0 .5 1 .0 CBFG(S) l o w - r e s o l u t i o n s u b p i x e l h i g h - r e s o l u t i o n The subpixel HCBF values are very close to the original high- resolution values.
  • 8. Contour Recognition for Isolated Objects Feature Vector Matching First identify the important features of the contour. Features are combined into a feature vector Characteristics of the contour. Type A critical points having smaller hexagonal CBA angles, Type B critical points are those with larger CBA angles. Threshold value, ψ = 120°
  • 9. Feature Vector Matching The feature vector is a six-digit numeral. First 2 digits are Type A critical points with positive and negative signs. Digits 3 and 4 are Type B critical points with positive and negative signs. Finally, digits 5 and 6 are of convex arcs and concave arcs, respectively.
  • 10. Similarity Matching  Similarity matching is to match two HCBF curves by directly measuring the differences between them. Similarity ratio, t t N S =Φ Data Window The HCBF of the sample The HCBF of the model The diagram of the similarity matching method
  • 11. Graph Matching for Occluded Objects The integrated method is used to find the corresponding pairs between the model graph and scene graph. Select Feature points Graph Matching The matching results are to be interpreted corresponding to different occurrences of every object model in the scene.
  • 12. Experimental Results Isolated Objects Feature vector Similarity ratio Model Sample Rectangular grid 324000 322000 86% Hexagonal grid 322000 324000 91% Hexagonal grid with subpixel technique 322010 322010 100% Due to the fact that the feature vectors of the model and the sample are not the same for rectangular grid and hexagonal grid without subpixel technique, the results of these feature vector matching are erroneous. Pixel Matching schemes
  • 13. Experimental Results  The cross-matching recognition is defined for arbitrarily two different objects that one object is a model and the other is a sample and vice versa. Fig: The shapes, the subpixel HCBFs and their corresponding feature codes of the patterns
  • 14. Experimental Results The similarity ratio Φ between models and samples It’s clearly seen that, object #1 is identical to #3 and #6, and is similar to #2, #4 and #9, but object #9 is similar to objects #1, #3, #5, #6, #8 and #12.
  • 15. Experimental Results Occluded Objects The model graphs and their extracted feature points in a low-resolution images The scene graphs and their extracted feature points in a low-resolution images
  • 16. Experimental Results Scene Resolution feature point Model matched point Pose (r, θ, tx, ty) Fig. 6.10(a) 42 x 62 16 Fig. 6.9(b) 9 1.01, 0.8, -1.2, 8.0 Fig. 6.9(e) 4 0.98, -33.4, -17.9, -12.6 Fig. 6.10(b) 55 x 58 17 Fig. 6.9(c) 5 1.04, -68.4, 44.0, 9.4 Fig. 6.9(e) 4 0.98, -33.4, -17.9, -12.6 Fig. 6.9(e) 5 1.05, -68.5, 4.4, 9.4 Fig. 6.10(c) 44 x 44 28 Fig. 6.9(a) 12 1.03, -61.2, -7.3, 9.9 Fig. 6.9(a) 12 1.05, 143.9, 0.3, 4.5 Fig. 6.10(d) 39 x 52 24 Fig. 6.9(d) 8 1.06, 60.4, -2.3, 0.5 Fig. 6.9(d) 6 0.85, -31.9, 3.0, 9.1 Fig. 6.9(d) 6 0.90, 170.8, -2.0, -8.9 The matching results of the proposed method on the low- resolution images From the table, it can be seen that multiple occurrences of the same object in one scene can be found simultaneously as well as their different poses.