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Image Matching using Local Symmetry

Features

Daniel Cabrini Hauagge

Noah Snavely

Cornell University

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Outline

Introduction Local Symmetry Scale Space Local Symmetry Features Experimental Results Conclusion

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Introduction

Analysis of symmetry :

A long –standing problem in computer vision.

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Introduction

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Local Symmetry

Method- takes an image as input, and computes local symmetry scores over the image and across scale space. Scoring local symmetries Gradient histogram-based score

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Local Symmetry

Bilateral symmetry

2n-fold rotational symmetry

For both symmetry types

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Local Symmetry

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Scoring local symmetries

Define our score Symmetry type

If the image f exhibits perfect symmetry types at location p, then f(q) = f(Ms,p(q)) for all q.

Distance function d(q,r)= | f(q)-f(r) |

Weight mask gives the importance of each set of corresponding poi

nt pairs around the center point p in determining the symmetry score at p.

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Scoring local symmetries

Define a function that we call the local symmetry distance

SS = L*SD

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Gradient histogram-based score

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Scale space

For the purpose of feature detection, we choose a different function for

r is the distance to the point of interest A is a normalization constant r0 is the ring radius ψ controls the width of the ring

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Scale space

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Local Symmetry Features

By finding local maxima of the score, and feature description, by building a feature vector from local symmetry scores Feature detector Feature descriptor

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Feature detector

Using the SYM-IR function as a detector. Represent the support of each feature as a ci

rcle of radius s centered at (x,y) in the original image.

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Feature detector

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Feature detector

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Feature descriptor

SYMD encodes the distribution of the three SYM-I scores around a feature location at the detected scale

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Experimental Results

Evaluate the detector, comparing its repeatability to that of the common DoG and MSER detectors. Evaluating detections Evaluating descriptors

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Evaluating detections

For each image pair(I1,I2) in the dataset, and each detector, we detect sets of keypoints K1 and K2 , and compare these detections using the known homography H12 mapping points from I1 to I2.

K1 is rescaled by a factor s so that it has a fixed area A ; we denote this scaled detection K1

S also applied to K2. Finally, the relative overlap of the support regions of H12K1

S and K2 gives an overlap score.

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Evaluating detections

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Evaluating detections

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Evaluating descriptors

A precision-call curve that summarizes the quality of the match scores.

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Evaluating descriptors

We generate two sets of perfectly matched synthetic detections by creating a set of keypoints K1 on a grid in I1 (in our experiments the spacing between points is 25 pixels and the scale of each keypoint is set to 6.25). We then map these keypoints to I2 using H12, creating a matched set of keys K2. We discard keypoints whose support regions are not fully within the image.

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Evaluating descriptors

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Evaluating descriptors

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Conclusion

To evaluate our method, we created a new dataset of image pairs with dramatic appearance changes, and showed that our features are more repeatable, and yield complementary information, compared to standard features such as SIFT.

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Thanks for your listening.