shape defined panoramas

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SHAPE DEFINED PANORAMASJohn Brosz & Faramarz SamavatiUniversity of Calgary

Shape Modeling International – June 2010

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Outline1. Scenario/Motivation2. Goals3. Related Work4. Observations5. Projection Surface Formulation6. Rendering7. Applications

Figure from Transformations & Projection in Computer Graphics, Salomon, Springer, 20064

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i = R

Figure from Transformations & Projection in Computer Graphics, Salomon, Springer, 2006

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z

j = +

( i, j ) = ( R ,

, + )Figure from Transformations & Projection in Computer Graphics, Salomon, Springer, 2006

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Spherical Projection Equation

( i, j ) =

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Goals

Create panoramas that:1. Allow for exploration &

customization2. Are defined by modeling3. Build on existing intuition4. Allow for visual understanding

Single Viewpoint: no “slit cameras”.

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Related WorkPanoramas from Perspective Images

Image from http://www.cirq.de/mosaicing.html

Image from Szeliski & Shum, Creating full view panoramic image mosaics and environment maps, Siggraph 1997

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Related WorkCorrecting Distortion

Images from Carrol, Agrawala & Agarwala, Optimizing Content-Preserving Projections for Wide-Angled Images, Siggraph 2009

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Related WorkSingle-Center Projections

Images from Trapp & Döllner, Generalization of Single-Center Projections Using Projection Tile Screens, VISIGRAPP, 2008

Normal Map

Panorama

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Common Panoramas

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Observations1. Shapes are associated with

panoramas

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Observations1. Shapes are associated with panoramas2. Angular change

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Observations1. Shapes are associated with panoramas2. Angular Change3. Parameterization is important

( i, j ) = ( R ,

, + )

( i, j ) =

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Shape Defined Panoramas

Defined by two curves1. Outline: closed, controls horizontal

sampling

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sampling

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sampling2. Profile: open, controls vertical

sampling

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sampling2. Profile: Open, controls vertical

sampling Curves parameterized by arc-length

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Shape Defined Panoramas Mix between surface of revolution

and surface extrusion

ProfileOutline

Extrusion Surface

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Shape Defined Panoramas Mix between surface of revolution

and surface extrusion

ProfileOutline

Panorama Surface

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Example 1

ProfileOutline

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Example 2

Outline

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Example 2Before

After

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Multiple Profiles

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Multiple Profiles

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Rendering

Ray-tracing Image Re-sampling Nonlinear Projection on GPU

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Rendering

Ray-tracing

x

x

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Rendering

Image Re-sampling

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Rendering

Nonlinear Projection on GPU

1. Find projection equation2. Project vertices with equation on GPU3. Be careful with seams

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Find Projection Equation

World Coordinates Normalized Device Coordinates

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Only surfaces that map onto spherical coordinates.

Projection Surface: Q(u,v) = (x,y,z) Projection Volume: t (0,0,0) + (1-t) Q(u,v)1. Find spherical coordinates of p = (x,y,z)2. Search for u,v s.t. Q(u,v) with same

spherical coords.3. t = || p ||

|| Q(u,v) ||

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Search for u,v s.t. Q(u,v) with same spherical coords.

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Project Vertices with GPU

Override projection matrix with nonlinear projection equation.

This only moves vertices! Triangles are filled as if linearly projected.

Nonlinearly ProjectedTriangle

Triangle w/ Linear Fill Algorithm

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Seams

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Seams

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Rendering Performance

Single pass algorithm 60 fps with 100K polygons on NVIDIA

8800 GTS

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Application:Custom Panorama

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Application:Re-projecting Panoramas

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Application:Animated Projection

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Application:Interactive Local Editing

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Application:Interactive Local Editing

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Conclusions

Use of modeling to define a projection. Use of Arc-length to dictate

parameterization. Visual means for creating panoramas. Realtime GPU based rendering of

panoramas.

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THANK-YOU

shape defined panoramas

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