Visibility Sorting and Compositing without Splitting for Image Layer Decompositions

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Visibility Sorting and Compositing without
Splitting for Image Layer Decompositions

• John Snyder, Jed Lengyel

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Layered Decomposition Problem

• Given set of moving geometric parts,
• and moving camera,
• find visibility ordering for every frame.

sort
composite
parts
sorted images
composited result
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Occlusion Cycles
split
group
When no order exists, can split or group parts.
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Non-Splitting Layered Decomposition

• Dont split parts that form occlusion cycles
• run-time splitting is slow
• splitting is often unnecessary
• splitting destroys coherence

Sorting requires no global separating plane.
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Image-Based Rendering AccelerationLengyel97
sprites
composited image
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Other Applications

• fast special effects
• animation playback with selective display
• incorporation of external image streams
• image stream compression
• fast hidden line rendering
• z resolution targeting

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Previous Work

• invisibility culling Greene93,Zhang97
• analytic hidden surface removal Mulmuley89
• global visibility Teller93,Durand97
• image layer decompositions
       Schumacker69,Newell72,Fuchs80
• dynamic visibility Torres90,Sudarsky96
• depth sorting for special effects Max85

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Occlusion Graphs

• pairwise occlusion relation A?E B
• relations on parts forms directed graph
     occlusion graph

A
B
view from E
side view
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Occlusion Graphs (Ex. 1)
A
B
A
B
C
C
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Occlusion Graphs (Ex. 2)
A
B
A
B
C
C
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Occlusion Graphs (Ex. 3)
A
B
C
Forms strongly connected component (SCC).
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Resolving Non-Binary Cycles
SCCs need not be rendered as an aggregate!
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Occlusion Testing via Collision
B
A
For convex hulls of objects A and B B?E A ?
ch(A? E) ? B ? ?
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Occlusion Testing via CollisionOccluding Example
B
ch(A? E) ? B ? ? ? B?E A
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Occlusion Testing via CollisionNon-Occluding
Example
B
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Trivial Sorting Algorithm

• compute occlusion graph
• detect and topologically sort SCCs
• at least quadratic in number of parts!

A
C
F
D
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Improving the Trivial Algorithm
A? B,C,D,F but nothing occludes A. Process A
first.
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Improving the Trivial Algorithm
A
C
F
D
Sorting Output A
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Improving the Trivial Algorithm
C
B
F
D
Sorting Output A, B
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Improving the Trivial Algorithm
C
F
D
Sorting Output A, B, C
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Improving the Trivial Algorithm
F
D
Sorting Output A, B, C, D, F
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Incremental Visibility Sort (IVS)

• similar to Newell, Newell, Sancha algorithm,
  1972
• sorts parts, not polygons
• detects SCCs, doesnt split
• uses order from last query, not depth order
• culls more efficiently using kd-tree

A
Z
B
Depth order doesnt indicate visibility order.
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IVS Algorithm

• While L is nonempty, pop off top element A
• if A is unmarked
• if nothing remaining on L occludes A
• send A to output
• else
• mark and reinsert A into L
• else // A is marked
• check for occlusion cycle
• if found, group cycle objects and reinsert
• else reinsert A into L

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Occlusion Culling

• Fundamental IVS query
• Which parts remaining in L occlude A?
• use convex hulls around parts
• bound hulls with spatial and angular extents
• occlusion cull reduces to 1D interval
  intersection
• bounded parts organized in dynamic kd-tree

object
kd extent
convex hull
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Spatial Extents
B ? A
B ? A
/
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Angular Extents
B ? A
B ? A
/
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Kd-Tree Occlusion Culling

• rebalance kd-tree every frame
• kd-tree supports part deactivation

x1
A
y2
y1
y1
y2
C
A
y
x1
x
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Exact Occlusion Testing

• Does B ? A?
• uses hybrid Chung/Gilbert collision algorithm
• requires extremal vertex query on A and B
• no need to create ch(A? E) dynamically
• exploits coherence in object motion

extremal vertex minimizes Dv on A
D
A
v
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Results (Video)
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IVS Complexity
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Performance with Increasing Objects
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Future Work

• animation previewer
• continuous time queries
• adaptive splitting, especially for terrain
• faster, less conservative visibility tests
• automatic part decomposition
• visibility sorting with minimal splitting

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Conclusions

• non-splitting layered decomposition useful
• software visibility sorting is practical
• basic ideas of approach
• exploit temporal and spatial coherence
• exploit properties of convex objects
• exploit incremental collision detection algorithms

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(No Transcript)
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Extent Tracking

• use vertex descent
• on convex polytope, local minimizer of extent is
  also    global minimizer

v1
D
v0
v0
frame t1
frame t0
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Results Tumbling Toothpicks

• eccentric ellipsoids moving in    cubical volume

• uniform scale (us) add more of same size
• biases occlusion complexity superlinearly
• uniform density (ud) add more of scaled size
• occlusion complexity increases linearly

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Performance with Increasing Velocity
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Performance with Increasing ObjectsUniform
Density Uniform Scale
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Kd-Tree Culling Performance
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Results Canyon Flyby

• six aircraft flying through valley
• investigates rendering acceleration at various
     levels of terrain splitting
• update rate assumptions
• aircraft parts 20
• terrain parts 70
• sky 40

• aggregation penalty   render every frame

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Results Canyon Flyby

• cpu times are in ms per frame
• update rate is poly-weighted

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Newell, Newell, Sancha (1972)

• traverse depth-sorted list of polygons
• if next polygon doesnt overlap, send to output
• otherwise use tests of increasing complexity
• screen bounding box, vertex/plane, 2d
  intersection
• if unoccluded, polygon is sent to output
• if occluded, polygon is marked and reinserted
• marked polygons are split to remove cycle

H
C
F
A
B
Z
G