Pattern Detection

Computer Vision

Some slides are from Yanxi Liu, CSE PennState Univ.

Correspondence Problem & Keypoint

Image Filters, Gradients, Image Processing

Blob Detectors, Edge, Corner, Key Points

Matching, Tracking, Homography

Shapes, Patterns (2D, 3D, Spatiotemporal)

Recognitions (Object, Face, Gesture, Instance, Scene)

Pattern Detection

Symmetry Pattern Detection

s

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Four Types of Primitive Symmetries

in 2D Euclidean Space [H. Weyl, 1952]

Rotation symmetry Translation symmetry Reflection symmetry

Glide-reflection symmetry

translation reflection

Reflection Symmetry Pattern Detection

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Curved Symmetry Axes are Everywhere!

Lizards & snakes

Leaves

Spines

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Related Work

Medial axis detection 2

Medial axis is not designed to find

(glide) reflection symmetries of the

pattern

[Peng et. al., Bioinformatics 08]

[Bonnassie et. al., ICIP 01]

Medial axis is not designed to find a

symmetry axis given discrete subparts

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Curved Glide-Reflection

Special cases of curved

glide-reflection symmetry

1. Reflection 2. Glide-reflection 4. Curved reflection 3. Non-Uniform

glide-reflection

Curved glide-reflection

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Axes Grouping

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Feature point

extraction

Matching point

pair selection

Curve fitting

Axes grouping

Axes grouping based

on the distance in 2D

density space

3D parameter

space

2d projection

Algorithm

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Curve Fitting

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Feature point

extraction

3D parameter

space

Axes grouping

Curve fitting -Fit 1~5 degree polynomial curves

Matching point

pair selection

Algorithm

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Curve Fitting With RANSAC

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Feature point

extraction

3D parameter

space

Axes grouping

Curve fitting

Matching point

pair selection

Algorithm

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Experimental Results

49 Zebra fish

Lizard

Leaves

Spine

Caterpillar

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Curved axis rectification

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Curved axis detection and rectification improves classification rate.

Quercus robur

Tilia

Sorbus aucuparia

Rotation Symmetry Pattern Detection

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Rotation Symmetry Groups

Cyclic group

Dihedral group Orthogonal group

[ 5 properties ] 1. Center of rotation

2. Affine deformation

3. Symmetry type

4. Cardinality

5. Supporting region

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Frieze-Expansion

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Frequency Analysis

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RSS

Affine

rectification

SSD LF

Frequency

analysis

Frieze-expansion

Merging &

elimination

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Experimental Results

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Real single-center images

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Experimental Results

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Real multi-center images