Low-Resolution Contour Recognition for Hexagonal Grid Images
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Low-Resolution Contour Recognition for Hexagonal Grid Images
ContentsIntroductionCurve Bend Function (CBF)Steps for obtaining HCBFSubpixel ImprovementContour Recognition for Isolated ObjectsGraph Matching for Occluded ObjectsExperimental 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=Nt, where J is an integer
called the supported length and is the supported rate, 0.01 0.05
The CBF of a point Si on Ω is defined as:), ()( J
iii cosrS g
Curve Bend Function (CBF) Contd..
The angle β is called the curve bend angle (CBA) at Si.
si-Jsi+J
si
β iJ
Ci
ρ S( i,Ci)
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 20 40 60 80 100
C ontour p ixels
-1.0
-0.5
0.0
0.5
1.0
CBF G
(S)
low -resolu tion su bp ixel h igh -resolu tion
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 20 40 60 80 100C ontour p ixels
-1.0
-0.5
0.0
0.5
1.0
CBF G
(S)
low -resolu tion su bp ixel h igh -resolu tion
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 vectorCharacteristics of the contour. Type A critical points having smaller hexagonal
CBA angles, Type B critical points are those with larger CBA
angles.Threshold value, = 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,
tt
NS
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 ResultsIsolated Objects
Feature vectorSimilarity 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 ResultsThe similarity ratio 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 ResultsOccluded 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 featurepoint 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, -12.6Fig. 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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