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− | * We must map from the Anchor Camera onto the plane. This gives us a | + | * We must map from the Anchor Camera onto the plane. This gives us a relation between angles on the panosphere and pixels on the plane . |

− | * We must map from the plane to Physical Camera 2. | + | * We must map from the plane to Physical Camera 2. This gives us a relation between pixels on the plane and the position of Physical Camera 2. |

## Revision as of 09:53, 1 June 2009

## Contents

# SoC2009 Dev Ghosh

## Abstract

Hugin creates wide-angle photo panoramas taken from a single camera position, one of the most popular applications of stitching software. However, when viewing a flat object such as a painting, photographs taken from different, casually chosen viewpoints must be combined to create a large high-resolution image mosaic. But Hugin can’t assemble photo mosaics of large flat objects photographed from many different camera locations. While tweaking Hugin’s settings can provide an approximate result, the underlying Panotools imaging model does not include a projective homography integrated with lens distortion correction. The optimize-able imaging parameters are unable to fully rectify and align the tiles of a mosaic image. This results in mosaics with warped edges and significant distortions. The process requires awkward user interactions as shown in [1], a tutorial by Joachim Fenkes titled “Creating linear panoramas with Hugin.” Fenkes uses horizontal image features such as utility boxes aligned at the same height along the graffiti covered wall to straighten the snaking panorama. I propose to add a new “mosaic mode” to Panotools. This will introduce a new image model based on multiple centers of projection to generate high-resolution, distortion-free images of flat objects captured with either handheld or tripod-mounted cameras.

[1] http://www.dojoe.net/tutorials/linear-pano/

## Details

Problem

Users of Hugin have developed methods for stitching 2D scanned objects and stitching linear panoramas. For best results, these methods rely on matching line constraints (control points of type horizontal or vertical line). But on images lacking clear horizontal or vertical features, when only manually placed or SIFT-generated control points are available, such approaches result in poorly aligned mosaics.

Solution

The Panotools imaging model optimizes eight parameters to correct lens distortion and geometric alignment. However, this model is unable to describe warps between overlapping images of a planar object taken from different viewpoints. While leaving the existing lens distortion parameters in place, I propose to develop an extended geometric model describing the relationship between a orthographic view of a planar object with a perspective view of a subsection of the object. This model will be optimized using the existing Levenberg-Marquardt optimizer. The optimized parameters will allow us to project each view of a subsection of the object as if it were viewed with a large, high-resolution, orthographic camera or with a perspective camera from a distance sufficient to view the whole. This approach will also allow views of the object taken from low angles to be projected and mapped to the orthographic view.

Performance Measures

The new geometric model will be tested on synthetic image data and overlapping views of a large painting in the collections at the Art Institute of Chicago. The results will be compared to those obtained using Panotools’s current model by average and worst control point distance and by image differencing in overlap regions.

## Project Timeline

I plan to spend at least 40 hours a week dedicated to this project. I have already begun to explore and make modifications to the source code. This head start will allow me to work through the months of April and May and continue through the end of Summer of Code. These are the steps I plan to take:

• Study current model for projection of images in libpano13 (prior to May 23)

• Research existing models for viewing images photographed from different viewpoints including “Gold Standard” Direct Linear Transform algorithm and Szeliski’s Image Alignment and Stitching: A Tutorial (prior to May 23)

• Develop geometric model for viewing of mosaic (two weeks)

• Implement new model in Panotools (five weeks)

• Test model on synthetic and real image data sets (two weeks)

• Evaluate performance by comparing alignment attempts with existing model (in average control point error) (two weeks)

• Wrap up and complete documentation (one week)

## Deliverables

• Documentation describing geometric model

• A library implementing the model

• Results of tests of library

• Fully-commented source code

## Biography

I have been experimenting with Hugin since Summer 2008 and started to build my own version and modify the source code in December 2008. I built Hugin both on Windows and on Linux under Ubuntu. My interest is in using Hugin to assemble large, high-resolution mosaics of paintings photographed from different viewpoints with 50% or more overlap.

I am a PhD candidate in Electrical Engineering and Computer Science at Northwestern University, Evanston, Illinois. I have coding experience in Python, C/C++, and MATLAB. My background is in video, signal, and image processing and my previous projects have included making improvements to the Joint Scalable Video Model, a scalable version of the H.264 video codec written in C++. I enjoy taking pictures and solving problems and participating in Google’s Summer of Code will allow me to work solely on this project over the summer without other distractions.

## References

• http://hugin.sourceforge.net/tutorials/scans/en.shtml

• http://www.dojoe.net/tutorials/linear-pano/

• Zhang, Z. and He, L.-W. (2007). Whiteboard scanning and image enhancement. Digital Signal Processing, 17(2), 414–432.

• http://www.ics.forth.gr/~lourakis/homest/

• http://grail.cs.washington.edu/projects/multipano/

• Richard Hartley and Andrew Zisserman (2003). Multiple View Geometry in computer vision. Cambridge University Press.

• Richard Szeliski (2006) Image alignment and stitching: a tutorial. Now Publishers Inc.

## Initial Approach

Below, we see a top view of the planar object we wish to image. The circle represents the panosphere and the triangles represent the viewing frusta of two cameras. We wish to project points on the planar object, (p(x,y)), as viewed from Physical Camera 2 to a virtual (output) Anchor Camera, coincident with Physical Camera 1.

To do this, we propose to add a position for each image (x,y,z). All images with non-zero (x,y,z) coordinates are projected to the plane. The location of the plane will be described by the yaw and pitch of a normal to the planar surface. (Note that Physical Camera 1/Anchor Camera is not necessarily perpendicular to the planar surface but it is located at (0,0,0) and is assumed to be 1 distance unit from the plane.)

Creating the output image takes two steps:

- We must map from the Anchor Camera onto the plane. This gives us a relation between angles on the panosphere and pixels on the plane .

- We must map from the plane to Physical Camera 2. This gives us a relation between pixels on the plane and the position of Physical Camera 2.