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Image Mosaicing

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Image Mosaicing

Shiran Stan-Meleh

*http://www.ptgui.com/info/image_stitching.html

Satellite Images

360 View

Panorama

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

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

Direct (appearance-based) methods

Manually…

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

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

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)

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

SIFT and RANSAC

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”

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

- 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

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

- 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

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

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

- 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

- 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

- 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

- 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

- Original image
- Low contrast removed (729)

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

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

- 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

- 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

- 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

- 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

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

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

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

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

- 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.

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

*copied from Hagit Hel-Or ppt

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

*copied from Hagit Hel-Or ppt

- 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

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

*copied from Hagit Hel-Or ppt

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

*copied from Hagit Hel-Or ppt

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

*copied from Hagit Hel-Or ppt

Repeat

C=3

*copied from Hagit Hel-Or ppt

Best Model

C=15

*copied from Hagit Hel-Or ppt

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

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

Challenges

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

Contenders for the crown

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

*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

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

- Why SIFT?

*A Comparison of SIFT, PCA-SIFT and SURF - Luo Juan & OubongGwun

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

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

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

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

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.

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

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

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

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

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.

Multi-Band Blending

Band 1 (scale 0 to σ)

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

2 Images

Extract Features

Match and filter using RANSAC

Transform and Blend

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

Image Matches

Connected components of image matches

Output panoramas

Question?

- 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

- 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