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Why do we need it?

Satellite Images

360 View

Panorama

- Compact Camera FOV = 50 x 35°
- Human FOV = 200 x 135°
- Panoramic Mosaic = 360 x 180°

How do we do it?

2 methods

- Direct (appearance-based)
- Search for alignment where most pixels agree

- Feature-based
- Find a few matching features in both images
- compute transformation

*Copied from Hagit Hel-Or ppt

How do we do it?

Direct (appearance-based) methods

Manually…

*http://www.marymount.fr/uploads/galleries/gallery402/images/002_matisse_project_gluing.jpg

How do we do it?

Direct (appearance-based) methods

- Define an error metric to compare the imagesEx: Sum of squared differences (SSD).
- Define a search technique (simplest: full search)
Pros:

- Simple algorithm, can work on complicated transformation
- Good for matching sequential frames in a video
Cons:

- Need to manually estimate parameters
- Can be very slow

How do we do it?

Feature based methods

- Harris Corner detection - C. Harris &M. Stephens (1988)
- SIFT - David Lowe (1999)
- PCA-SIFT - Y. Ke & R. Sukthankar (2004)
- SURF - Bay & Tuytelaars (2006)
- GLOH - Mikolajczyk & Schmid (2005)
- HOG - Dalal & Triggs (2005)

Agenda

We will concentrate on feature based methods using SIFT for features extraction and RANSAC for features matching and transformation estimation

Some Background

SIFT and RANSAC

What is SIFT?

Scale Invariant Features Transform

From Wiki: “an algorithm in computer vision to detect and describe local features in images. The algorithm was published by David Lowe in 1999”

Applications

- Object recognition
- Robotic mapping and navigation
- Image stitching
- 3D modeling
- Gesture recognition
- Video tracking
- Individual identification of wildlife
- Match moving

Basic Steps

- Scale Space extrema detection
- Construct Scale Space
- Take Difference of Gaussians
- Locate DoG Extrema

- Keypoint localization
- Orientation assignment
- Build Keypoint Descriptors

*http://www.csie.ntu.edu.tw/~cyy/courses/vfx/05spring/lectures/handouts/lec04_feature.pdf

1a. Construct Scale Space

Motivation:

Real-world objects are composed of different structures at different scales

First Octave

Explanation:

representing an image at different scales at different blurred levels

Second Octave

*copied from Hagit Hel-Or ppt

1b. Take Difference of Gaussians

- Experimentally, Maxima of Laplacian-of-Gaussian (LoG: ) gives best notion of scale:
- But it’s extremely costly so instead we use DoG:

*Distinctive Image Features from Scale-Invariant Keypoints David G. Lowe

*Mikolajczyk 2002

1c. Locate DoG Extrema

- Find all Extrema, that is minimum or maximum in 3x3x3 neighborhood:

*Distinctive Image Features from Scale-Invariant Keypoints David G. Lowe

Basic Steps Orientation assignment Build Keypoint Descriptors

- Scale Space extrema detection
- Keypoint localization
- Sub Pixel Locate Potential Feature Points
- Filter Edge and Low Contrast Responses

*http://www.csie.ntu.edu.tw/~cyy/courses/vfx/05spring/lectures/handouts/lec04_feature.pdf

2a. Sub Pixel Locate Potential Feature Points

- Problem:
- Solution:Take Taylor series expansion:Differentiate and set to 0 to get location in terms of :

*http://www.inf.fu-berlin.de/lehre/SS09/CV/uebungen/uebung09/SIFT.pdf

2b. Filter Edge and Low Contrast Responses

- Remove low contrast points (sensitive to noise):
- Remove keypoints with strong edge response in only one direction (how?):

*http://www.inf.fu-berlin.de/lehre/SS09/CV/uebungen/uebung09/SIFT.pdf

2b. Filter Edge and Low Contrast Responses

- By using Hessian Matrix:
- Eigenvalues of Hessian matrix are proportional to principal curvatures
- Use Trace and Determinant:
- R=10, only 20 floating points operations per Keypoint

“Picture worth a 1000 keypoints”

- Original image
- Low contrast removed (729)

- Initial features (832)
- Low curvature removed (536)

*Distinctive Image Features from Scale-Invariant Keypoints David G. Lowe

Basic Steps

- Scale Space extrema detection
- Keypoint localization
- Orientation assignment
- Build Keypoint Descriptors

Low contrast removed

Low curvature removed

*http://www.csie.ntu.edu.tw/~cyy/courses/vfx/05spring/lectures/handouts/lec04_feature.pdf

3. Orientation assignment

- Compute gradient magnitude and orientation for each SIFT point :
- Create gradient histogram weighted by Gaussian window with = 1.5* and use parabola fit to interpolate more accurate location of peak.

*http://www.inf.fu-berlin.de/lehre/SS09/CV/uebungen/uebung09/SIFT.pdf

Basic Steps

- Scale Space extrema detection
- Keypoint localization
- Orientation assignment
- Build Keypoint Descriptors

*http://www.csie.ntu.edu.tw/~cyy/courses/vfx/05spring/lectures/handouts/lec04_feature.pdf

4. Build Keypoint Descriptors

- 4x4 Gradient windows relative to keypoint orientation
- Histogram of 4x4 samples per window in 8 directions
- Gaussian weighting around center( is 0.5 times that of the scale of a keypoint)
- 4x4x8 = 128 dimensional feature vector
- Normalize to remove contrast
- perform threshold at 0.2 and normalize again

*Image from: Jonas Hurrelmann

Live DemoAnd next…RANSAC

*http://habrahabr.ru/post/106302/

What is RANSAC?

RANdom SAmple Consensus

- first published by Fischler and Bolles at SRI International in 1981
- From Wiki:
- An iterative method to estimate parameters of a mathematical model from a set of observed data which contains outliers
- Non Deterministic
- Outputs a “reasonable” result with certain probability

What is RANSAC?

A data set with many outliers for which a line has to be fitted

Fitted line with RANSACoutliers have no influence on the result

*http://en.wikipedia.org/wiki/RANSAC

RANSAC Input & Output

The procedure is iterated k times, for each iteration:

- Input
- Set of observed data values
- Parameterized model which can explain or be fitted to the observations
- Some confidence parameters

- Output
- Best model - model parameters which best fit the data (or nil if no good model is found)
- Best consensus set - data points from which this model has been estimated
- Best error - the error of this model relative to the data

Basic Steps

- Select a random subset of the original data called hypothetical inliers
- Fill free parameters according to the hypothetical inliers creating suggested model.
- Test all non hypothetical inliers in the model, if a point fits well, also consider as a hypothetical inlier.
- Check that suggested model has sufficient points classified as hypothetical inliers.
- Recheck free parameters according to the new set of hypothetical inliers.
- Evaluate the error of the inliers relative to the model.

Basic Steps – Line Fitting Example

- Select a random subset of the original data called hypothetical inliers

*copied from Hagit Hel-Or ppt

Basic Steps – Line Fitting Example

- Fill free parameters according to the hypothetical inliers creating suggested model.

*copied from Hagit Hel-Or ppt

Basic Steps – Line Fitting Example

- Test all non hypothetical inliers in the model, if a point fits well, also consider as a hypothetical inlier.

*copied from Hagit Hel-Or ppt

Basic Steps – Line Fitting Example

- Check that suggested model has sufficient points classified as hypothetical inliers.
C=3

*copied from Hagit Hel-Or ppt

Basic Steps – Line Fitting Example

- Recheck free parameters according to the new set of hypothetical inliers.
C=3

*copied from Hagit Hel-Or ppt

Basic Steps – Line Fitting Example

- Evaluate the error of the inliers relative to the model.
C=3

*copied from Hagit Hel-Or ppt

An example from image mosaicing

Estimate transformation

Taking pairs of points from 2 images and testing with transformation model

- Model: direct linear transformation
- Set size: 4
- Repeats: 500
- Thus for the probability that the correct transformation is not found after 500 trials is approximately

How it is done?

For each pair of images:

- Extract features
- Match features
- Estimate transformation
- Transform 2nd image
- Blend two images
- Repeat for next pair

*Automatic Panoramic Image Stitching using Invariant Features M. Brown * D.G. Lowe

1. Extract features

Challenges

- Need to match points from different images
- Different orientations
- Different scales
- Different illuminations

1. Extract features

Contenders for the crown

- SIFT - David Lowe (1999)
- PCA-SIFT - Y. Ke & R. Sukthankar (2004)
- SURF - Bay & Tuytelaars (2006)

1. Extract features

*http://homepages.dcc.ufmg.br/~william/papers/paper_2012_CIS.pdf SIFT or PCA-SIFT

- Used to lower the dimensionality of a dataset with a minimal information loss
- Compute or load a projection matrix using set of images which match a certain characteristics

1. Extract features

Principal Components Analysis SIFT or PCA-SIFT

- Detect keypoints in the image same as SIFT
- Extract a 41×41 patch centered over each keypoint, compute its local image gradient
- Project the gradient image vector by multiplying with the projection matrix - to derive a compact feature vector.
- This results in a descriptor of size n<20

How it is done?

For each pair of images:

- Extract features
- Match features
- Estimate transformation
- Transform 2nd image
- Blend two images
- Repeat for next pair

*Automatic Panoramic Image Stitching using Invariant Features M. Brown * D.G. Lowe

2. Match features

General approach

- Identify K nearest neighbors for each keypoint (Lowe suggested k=4) where…
- Near is measured by minimum Euclidian distance between a point (descriptor) on image A to points (descriptor) in image B.
- Takes complexity thus using k-d tree to get

2. Match features

Another approach

- For each feature point define a circle with the feature as center and r=0.1*height_of_image
- Find largest Mutual Information value between a circle of feature in image A to a circle of feature in image B:
- H is the Entropy of an image block

*Image Mosaic Based On SIFT - PengruiQiu,YingLiangandHuiRong

How it is done?

For each pair of images:

- Extract features
- Match features
- Estimate transformation
- Transform 2nd image
- Blend two images
- Repeat for next pair

*Automatic Panoramic Image Stitching using Invariant Features M. Brown * D.G. Lowe

3. Estimate transformation

Problem:

- Outliers: Not all features has a match, why?
- They are not in the overlapped area
- Same features were not extracted on both images
Solution... RANSAC

- Decide on a model which suits best.
- Input the model, size of set, number of repeats, threshold and tolerance.
- Get a fitted model and the inliers feature points.

How it is done?

For each pair of images:

- Extract features
- Match features
- Estimate transformation
- Transform 2nd image - Depending on the desired output (panorama, 360 view etc.) and transformation found
- Blend two images
- Repeat for next pair

*Automatic Panoramic Image Stitching using Invariant Features M. Brown * D.G. Lowe

How it is done?

For each pair of images:

- Extract features
- Match features
- Estimate transformation
- Transform 2nd image
- Blend two images
- Repeat for next pair

*Automatic Panoramic Image Stitching using Invariant Features M. Brown * D.G. Lowe

5. Blend two images

Simple approach

- Place 2nd image on top of reference image.
- Apply weighted average on pixel values in overlapping area:

*http://inside.mines.edu/~whoff/courses/EGGN512/projects/2012/Photomosaic%20Image%20Stitching%20Using%20SIFT%20Features.pdf

5. Blend two images

Pyramid Blending

- Create Laplacian pyramid for each image
- Combine the two images in different Laplacian levels by combining partial images from each of them

*http://inside.mines.edu/~whoff/courses/EGGN512/projects/2012/Photomosaic%20Image%20Stitching%20Using%20SIFT%20Features.pdf

5. Blend two images

Multi-Band Blending

- Burt and Adelson [BA83].
- The idea behind multi-band blending is to blend low frequencies over a large spatial range, and high frequencies over a short range.

5. Blend two images

Multi-Band Blending

Band 1 (scale 0 to σ)

*Automatic Panoramic Image Stitching using Invariant Features M. Brown * D.G. Lowe

Extract Features

Match and filter using RANSAC

Transform and Blend

*Automatic Panoramic Image Stitching using Invariant Features - M Brown and DG. Lowe

Idea – Millions of images

Image Matches

Idea – Millions of images

Connected components of image matches

Idea – Millions of images

Output panoramas

That’s it…

Question?

References - Articles

- http://inside.mines.edu/~whoff/courses/EGGN512/projects/2012/Photomosaic%20Image%20Stitching%20Using%20SIFT%20Features.pdf
- http://pages.cs.wisc.edu/~csverma/CS766_09/ImageMosaic/imagemosaic.html
- “Image Mosaic Based On SIFT”, Yang zhan-long and Guobao-long.International Conference on Intelligent Information Hiding and Multimedia Signal Processing, pp:1422-1425,2008.
- Image Mosaics Algorithm Based on SIFT Feature Point Matching and Transformation Parameters Automatically Recognizing - PengruiQiu,Ying Liang and HuiRongwww.atlantis-press.com/php/download_paper.php?id=4823
- Image Alignment and Stitching: A Tutorial1 - Richard Szeliskihttp://sse.tongji.edu.cn/linzhang/computervision/projects/image%20alignment%20and%20stitching%20a%20tutorial.pdf
- Comparison of SIFT SURFhttp://www.cscjournals.org/csc/manuscript/Journals/IJIP/volume3/Issue4/IJIP-51.pdf

References - Additional

- http://en.wikipedia.org/wiki/Scale-invariant_feature_transform
- http://www.scholarpedia.org/article/SIFT
- “SIFT: scale invariant feature transform by David Lowe” - Presented by Jason Clemonshttp://web.eecs.umich.edu/~silvio/teaching/EECS598/lectures/lecture10_1.pdf
- “SIFT - The Scale Invariant Feature Transform” - Presented by Ofir Pelehttp://www.inf.fu-berlin.de/lehre/SS09/CV/uebungen/uebung09/SIFT.pdf
- http://en.wikipedia.org/wiki/RANSAC
- http://www.computerrobotvision.org/2010/tutorial_day/tam_surf_rev3.pdf
- http://www.cs.cmu.edu/~rahuls/pub/cvpr2004-keypoint-rahuls.pdf

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