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 . .