An Analytical Model for Progressive Mesh Streaming

1
An Analytical Model for Progressive Mesh
Streaming

• Wei Cheng, Wei Tsang Ooi
• School of Computing, National University of
  Singapore.
• Sebastian Mondet, Romulus Grigoras,
• Geraldine Morin,
• IRIT/ENSEEIHT, France.

2
Outline

• Background and motivation of our research
• An analytical model for progressive mesh
  streaming
• The main insight from the model
• A sending strategy based on our model

3
Applications of 3D Streaming

• Virtual Museums
• e.g. UC Davis Geology Department

4
Applications of 3D Streaming

• Virtual Reality / Games
• Second Life
• Active Worlds

5
Huge Amount of Data
4.9 MB
14 MB
155 MB
2 GB
Models from http//www-graphics.stanford.edu/
6
Progressive Streaming
7
Progressive Mesh (Hoppe 96)

• Based on edge collapse

A series of edge collapses
A series of vertex splits
8
Progressive Streaming

• Base mesh a series of vertex splits

Base mesh
vs1
vs2
vs3
vs4
vs5
vs6
vs7
vs8
9
Dependency Among Vertex Splits

• Vertex to be split should exist.
• The four neighbor faces should exist to avoid
  illegal split.

V2
V1
V3
V1
V2
V3
V4
V5
V
V
V5
V4
10
Representation of Dependency

• Directed acyclic graph (DAG)

directed acyclic graph
Vertex split
dependency
11

• What is the
• Research Question?

12
The Research Question

• Effect of dependency on video streaming is well
  known.
• What is the effect of vertex split dependencies
  on progressive mesh streaming?

13
Property 1

• Longer chain of dependencies than in video.

I
B
P
B
P
B
P
I
B
P
B
P
B
P
Progressive Mesh
MPEG1
14
Retransmission is Needed

• One packet loss may disable the decoding of many
  subsequent vertex splits.
• Retransmission is important.

15
Importance of a Vertex Split

• The increase in mesh quality after decoding this
  vertex split.
• Any quality metric can be used in our model, e.g.
• Hausdorff distance
• View dependent metrics

16
Property 2

• The importance of vertex splits decreases quickly.

importance
Vertex splits
17
Retransmission Has Higher Priority

• When we need to choose between retransmission and
  sending new data, it is better to retransmit lost
  packet.
• Because the older data is typically more
  important.

18
Case1 all following packets dependent on the
lost packet Case2 all following packets are
independent.
packet 1 is lost
quality
Case 2
time
Case 1
packet 1 is retransmitted
19
Quality Curve

• Objective is to improve the quality on the client
  side.
• The quality changes with time.

20
Our Objective

• Analytically estimate the cumulative quality of
  the decoded mesh at a given time t (area under
  the curve).

quality
time
21
Decoded Mesh Quality
quality

• Area under the curve

wv
time
0
Dv
t
22
The Key is Dv

• Dv is a random variable since packet loss is
  random.
• Need to find EDv for each vertex split.
• Dv depends on
• Loss rate (channel property)
• Dependencies among data (data property)

23
Outline

• Background and motivation of our research
• An analytical model for progressive mesh
  streaming
• The main insight from the model
• A sending strategy based on our model

24
Assumptions

• UDP retransmission
• Constant sending rate
• We Retransmit lost packet as soon as packet loss
  is detected.
• Packet loss is detected after time Td.

Si
Td
Td
25
Time

• Receivers clock begins RTT/2 later (if packet is
  not lost, the sending time the receiving time).
• One unit time time to send a packet.
• If no retransmission, sending time sequence
  number.

t 0
0
t 0
t i
i
t i
26
Steps

• Find the distribution of
• sending time
• receiving time
• decoding time

27
Sending Time

• Sending Time Si is a random variable with
  Negative Binomial Distribution.

Td the time to detect packet loss p the loss
rate
28
Receiving Time Ri

• Ri Si nTd if it is retransmitted n times.
• n is a random variable with geometric
  distribution.
• We approximate Si using ESi.
• Ri ESi nTd
• The distribution of Ri can be computed.
• See the paper for detail.

Si
Td
Td
Si 2Td
Si 2Td
29
Decoding Time Dv

• If an ancestor of vertex split v is inside a
  packet p, we say p is a parent packet of v.
• Vertex split v can only be decoded when all
  packets in P(v) are received.
• P(v) the set of packet i and all parent packets
  of vertex v.
• Vertex v is in packet i

P(v)
Packet i
Vertex v
30
Decoding Time Dv

Packet j received at t
Others received before t
In practice, we only consider j from Si to Si
3Td.
31
After knowing Dv

• We can estimate the expected value of quality of
  a given 3D mesh as a function of time and packet
  loss probability.

32
Verification of Dv

• We made two approximations
• We use ESi to replace random variable Si in
  calculating Ri.
• We only add up to Si 3Td instead of infinity in
  calculating EDv.
• We use simulation to verify the accuracy after
  our approximations.
• The difference between analytical result and
  simulation result is very small.
• 0.1223 in average
• 1.3083 in maximum
• (100000runs of simulation, loss rate 10)

33
Outline

• Background and motivation of our research
• An analytical model for progressive mesh
  streaming
• The main insight from the model
• A sending strategy based on our model

34
Sending Strategy and Quality Curve

• Quality curve depends on Dv.
• Dv depends on the sending order and dependency.
• Sending strategy decides the sending order and
  hence the dependency among packets.
• Different sending strategies generate different
  quality curves.

35
How much can we improve the quality if we choose
a proper sending strategy?
36
Consider Two Extreme Cases

• Worst Case vs. Ideal Case

37
Worst Case vs. Ideal Case
38
The Main Insight

• The effect of dependency is only significant in
  the first few seconds.
• Need to deal with dependencies only for
  interactive applications where this first few
  seconds matter
• E.g., online games, building walkthrough

39
What can we do?

• Use a better sending strategy.
• Consider the effect of dependency
• Increase the initial sending rate
• Add FEC to initial data
• Our model can be used to make the proper
  trade-off in all above cases.

40
Outline

• Background and motivation of our research
• An analytical model for progressive mesh
  streaming
• The main insight from the model
• A sending strategy based on our model

41
Greedy Strategy

• We can calculate Dv.
• gainwv(Dv-Dv)
• Pack the vertex split with the maximum gain.

v
?
?
Dv
Dv
Next Packet
Current Packet
42
Comparison of Greedy and FIFO

• FIFO
• Send the vertex splits in first-in-first out
  order (typically in the decreasing order of
  importance).
• Greedy
• Consider both importance and dependency.

gainwv (Dv-Dv)
importance
Effect of dependency
43
Average Quality (Td 40, p 0.1)
44
In 90 Cases, the quality is better than(Td
40, p 0.1)
45
Results
Greedy
FIFO
46
Conclusion

• Retransmission is important in Progressive mesh
  streaming.
• The effect of packet loss exists even with
  retransmission and it depends on the dependency.
• The effect of dependency is significant in first
  few seconds.
• We can improve the initial quality with better
  strategy than FIFO.

47
Thank You! Q A Time
48
Results
FIFO average
Greedy 90 cases
Greedy average
FIFO 90 cases