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Symmetric Architecture Modeling with a Single ImagePowerPoint Presentation

Symmetric Architecture Modeling with a Single Image

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Symmetric Architecture Modeling with a Single Image

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Symmetric Architecture Modeling with a Single Image

Author: Nianjuan Jiang, Ping Tan, Loong-Fah Cheong

Department of Electrical & Computer Engineering, National University of Singapore

Presenter: Feilong Yan

Model architecture from single image is common task in 3D creation due to the lack of the more images.

Historic Photo:

Internet Photo:

Single image based modeling is very difficult!

Due to the trouble on camera calibration and texture loss

The recent methods only can handle simple and planar façade

Pascal Mulleet al. Image-based procedural modeling of facades

Changchang Wu et al. Repetition-based Dense Single-View Reconstruction

But what about this one?

And If we only have this single photo.

Complex and not planar

Fortunately , the symmetry is very prevalent in the architecture

Symmetry is a breakthrough which magically can generate

more images from the input

Complex and not planar

This is reasonable, but exciting to me

Bilateral Symmetry

Rotational Symmetry

2 even more views Reconstruction

3D Reconstruction

Surface Modeling

Texture Enhancement

Input Image and Frustum Vertices

Model Refinement

Model Initialization

Calibration and 3D Reconstruction

Camera Calibration

3D points Reconstruction

Previous Methods

Calibrate the camera from the vanishing points of 3 mutually orthogonal directions in a single image.

HARTLEY, R., AND ZISSERMAN

Multiple View Geometry in Computer Vision

But many photos do not have 3 vanishing points, and this method is often numerical unstable

Previous Methods

If enough(>=6) correspondences between spatial vertices and the image pixels are known, the camera calibration may be immediately computed.

WILCZKOWIAK, M. et. al Using geometric constraints through parallelepipeds for calibration and 3d modeling

Parallelipiped is used to represent a building block. Under the constraint of parallelipiped, the visible 6 spatial vertices may be estimated.

This method is stable but not very suitable for some architecture

New Method:

Inspired by parallelipiped method, the author found the frustum more general to represent the architecture

Demo:

Frustum is symmetric

6

4

5

3

1

2

Coordinate represented in world:

Of this example

6

4

5

3

1

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K=

=

= Quaternion( unit vector(x,y,z),)

t =t(x, y, z)

15 parameters to estmate

=1

6

4

5

3

1

2

Simplification:

K=

11 parameters to estimate, now the calibration is formulated as a non-linear optimization

Optimization Initialization:

=

=

The Quadratic :

Extend the right multiplication, since the R is unit orthogonal matrix, then we obtain:

User gives the

Symmetry-Based Triangulation:

Symmetry-Based Triangulation:

User-Interaction Assisted Modeling

Geometry Modeling

Model Refinement

Texture Mapping

Roof

Planar Structure

Single image inevitably lack texture samples due to the foreshortening and occlusion.

But to achieve a good texture effect, there are 2 requirements:

1. the final texture should be consistent with the foreshortened image ;

2, the final texture should have consistent weathering pattern.

We need to know where is well textured and where not

Refine low quality region

Detect Texture Quality

Texture the occluded region

Back Project

Ratio = Triangle.size / imageProjection.size

Ratio > Threshold and Ratio is finite: large texture distortion

Ratio<Threshold: distortion free

Ratio is infinite: occluded

Texture in distortion free region will be used as the texture sample

Super- Resolution Problem

The simplest way is to repeat the same texture as those of their symmetric counterparts, but this makes the model look artificial.

It is better to synthesize the texture in these region with common method

Another feature of the texture is weathering pattern, a constraint texture map is used according to the height of the architecture.

Synthesized

Input sample

- Contribution:
- Novel Calibration Method
- Texture Enhance Method

- Limitations:
- Strong assumption for simplification of camera calibration