Symmetric Architecture Modeling with a Single Image

Author: Nianjuan Jiang, Ping Tan, Loong-Fah CheongDepartment of Electrical & Computer Engineering, National

University of Singapore

Presenter: Feilong Yan

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

Historic Photo:

Internet Photo:

MotivationSingle 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 Mulle et al. Image-based procedural modeling of facades

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

Motivation

But what about this one?And If we only have this single photo.

Complex and not planar

Motivation

Fortunately , the symmetry is very prevalent in the architecture

Complex and not planar

Symmetry is a breakthrough which magically can generate more images from the input

This is reasonable, but exciting to me

Main IdeaBilateral Symmetry

Main IdeaRotational Symmetry

Main Idea2 even more views

Reconstruction

Modeling Pipeline

Input Image and Frustum Vertices

Calibration and 3D Reconstruction

Model Initialization

Texture Enhancement

Model Refinement

3D Reconstruction Surface Modeling

3D ReconstructionCamera Calibration 3D points

Reconstruction

Camera CalibrationPrevious Methods

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

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

HARTLEY, R., AND ZISSERMAN Multiple View Geometry in Computer Vision

Camera CalibrationPrevious Methods

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

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

This method is stable but not very suitable for some architecture

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

Camera CalibrationNew Method:

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

Camera CalibrationDemo:

Frustum is symmetric

Camera Calibration

𝛬=(𝑙1 𝑙2 cos𝜃 0 00 𝑙2 sin 𝜃 0 0

0 0𝑙3𝛼 0

0 0 1𝛼 1 )𝑃 𝑖=𝛬⋅ �̂� 𝑖 ¿

1 2

4

3

56

Coordinate represented in world:

𝑥 ,𝑖❑ 𝑦 𝑖∈ {1 ,−1} 𝑧𝑖∈ {0,1 }

𝛬=(𝑙1         0 0 00         𝑙2 0 0

0 0𝑙3𝛼 0

0 0 1𝛼 1 )Of this example

Camera Calibration

¿1 2

4

3

56

𝑝𝑖≃𝑀𝑃 𝑖=𝑀 𝛬 �̂�𝑖=�̂� �̂� 𝑖

M=K ⋅ [R|t ] ¿

=

K=

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

t =t(x, y, z)

15 parameters to estmate =1 𝑙1 𝑙2 𝜃𝛼❑

Camera Calibration

1 2

4

3

56

K=

Simplification:

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

Camera CalibrationOptimization Initialization:

= =

The Quadratic :

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

1 22 2 2ˆ ˆ( )T Tm K K m l

�̂�1𝑇 (𝐾 −𝑇 ⋅ 𝐾− 1)�̂�1=𝑙12

�̂�1𝑇 (𝐾 −𝑇 ⋅ 𝐾− 1)�̂�2=𝑙1𝑙2cos𝜃

�̂�2𝑇 (𝐾 −𝑇 ⋅ 𝐾− 1)�̂�2=𝑙22

User gives the

3D Points ReconstructionSymmetry-Based Triangulation:

3D Points ReconstructionSymmetry-Based Triangulation:

Surface Modeling

Geometry Modeling Model Refinement Texture Mapping

User-Interaction Assisted Modeling

Geometry ModelingPlanar Structure

Roof

Model Refinement

Texture MappingSingle 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.

Detect Texture Quality

Refine low quality region

Texture the occluded region

We need to know where is well textured and where not

Texture Quality Detection

Back Project

Ratio = Triangle.size / imageProjection.size

Ratio > Threshold and Ratio is finite: large texture distortionRatio<Threshold: distortion freeRatio is infinite: occluded

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

Refinement for Low-Quality

Super- Resolution Problem

Occluded Region TexturingThe 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.

Input sample Synthesized

Result

Result

Conclusion

• Contribution:– Novel Calibration Method– Texture Enhance Method

• Limitations:– Strong assumption for simplification of

camera calibration

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