Object Removal in Multi-View Photos

Image Rectification

Image Rectification

Figure 1: Example rectification of source images (1) to common image plane (2). 1

Transformation process used to project two-or-more images onto a common image plane.

Corrects image distortion by transforming the image into a standard coordinate system. 1

Image Rectification

To perform a transform...

Cameras are calibrated and provide internal parameters resulting in an essential matrix representing relationship between the cameras.– We don’t have access to camera’s internal parameters.– What if single camera was used?

The more general case (without camera calibration) is represented by the fundamental matrix. 2

Fundamental Matrix

Algebraic representation of epipolar geometry.

3×3 matrix which relates corresponding points in stereo images.

7 degrees of freedom, therefore at least 7 correspondences are required to compute the fundamental matrix. 3

Corresponding Points

Figure out which parts of an image correspond to which parts of another image.– But what is a ‘part’ of an image?

‘part’ of an image is a Spatial Feature.

Spatial Feature Detection is the process of identifying spatial features in images.

Spatial Feature Detection - Edges

Canny, Prewitt, Sobel, Difference of Gaussians...

Figure 2: Example application of Canny Edge Detection 4

Spatial Feature Detection - Corners

Harris, FAST, SUSAN

Figure 2: Example application of Harris Corner Detection 5

Feature Description

Simply identifying a feature point is not in itself useful.– consider how one would attempt to match detected

feature points between multiple images.

Scale-invariant feature transform (SIFT) offers robust feature description. 6

– Invariant to scale– Invariant to orientation– partially invariant to illumination changes

SIFT

Uses Difference of Gaussians along with multiple smoothing and resampling filters to detect key points (Feature Points with descriptor data)

Key point specifies 2D location, scale, and orientation.

SIFT

Figure 3: Sample image for SIFT application

SIFT – Feature Points

Figure 4: Detected feature points via SIFT

SIFT – Key Point

Figure 5: A SIFT key point in detail.

SIFT - Matching

Matching SIFT key points by identifying nearest neighbour with the minimum Euclidean distance.

Ensures robustness via... Cluster identification by Hough transform voting. Model verification by linear least squares.

SIFT - Matching

Figure 5: Example of matched SIFT key points. Note its tolerance to image scale and rotation.

SIFT – Suitable for Multi-View?

SIFT fails to accurately match key points between images which vary significantly in perspective.

Figure 7 & 8: Comparison of SIFT accuracy with varying perspective angles.

Left image is 45 degrees with 152 matches.

Right image is 75 degrees with 11 matches.

SIFT – Suitable for Multi-View?

SIFT fails to accurately match key points between images which undergo non-scalable affine transformation or projection.

Figure 9: SIFT fails to identify any key point matches between rotated images on a cylinder.

ASIFT

A new framework for fully affine invariant image comparison.

Uses existing SIFT key point descriptors, but matching algorithm has improved.

ASIFT – Improvements over SIFT

Simulated images are compared by a rotation, translation and zoom-invariant algorithm.– (SIFT normalizes translation and rotation and simulates

zoom.)

ASIFT – Improvements over SIFT

Figure 10: ASIFT (left) identifies 165 matches compared to SIFT’s 11 on surface rotated 75 degrees

ASIFT – Improvements over SIFT

Figure 10: ASIFT identifies 381 matches between rotated surfaces.

Image Rectification

Quick Review...

1. Given multiple images of the same scene from different perspectives...

2. We have identified & matched feature points using ASIFT.

3. We now have the ability to calculate the fundamental matrix.

Calculating Fundamental Matrix

References

1. Oram, Daniel (2001). "Rectification for Any Epipolar Geometry“2. Fusiello, Andrea (2000-03-17). "Epipolar Rectification".

http://profs.sci.univr.it/~fusiello/rectif_cvol/rectif_cvol.html.3. Richard Hartley and Andrew Zisserman (2004). “Multiple View Geometry in

Computer Vision Second Edition”4. Ma,Yi. (1996) Basic Image Processing Demos (for EECS20)

http://robotics.eecs.berkeley.edu/~sastry/ee20/index.html 5. Mark Nixon & Alberto Aguado (2002), Feature Extraction & Image Processing,

Newnes6. Lowe, D. G., “Distinctive Image Features from Scale-Invariant Keypoints”,

International Journal of Computer Vision, 60, 2, pp. 91-110, 2004.