An Analytical Model for Progressive Mesh

Streaming

Wei Cheng, Wei Tsang OoiSchool of Computing, National University of Singapore.

Sebastian Mondet, Romulus Grigoras,Geraldine Morin,IRIT/ENSEEIHT, France.

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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

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Applications of 3D Streaming

Virtual Museums e.g. UC Davis Geology Department

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Applications of 3D Streaming

Virtual Reality / Games: Second Life Active Worlds

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Huge Amount of Data

4.9 MB14 MB

155 MB

2 GB

Models from http://www-graphics.stanford.edu/

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Progressive Streaming

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A series of edge collapses

A series of vertex splits

Progressive Mesh (Hoppe ‘96)

Based on edge collapse

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Basemesh

vs1 vs2 vs3 vs4 vs5 vs6 vs7 vs8

Progressive Streaming

Base mesh + a series of vertex splits

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Vertex to be split should exist. The four neighbor faces should exist

to avoid illegal split.

V

V1V2V3

V4 V5

V1 V2 V3 V4 V5

V

Dependency Among Vertex Splits

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Directed acyclic graph (DAG)

directed acyclic graph

Vertex split dependency

Representation of Dependency

What is the Research Question?

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The Research Question

Effect of dependency on video streaming is well known.

What is the effect of vertex split dependencies on progressive mesh streaming?

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Longer chain of dependencies than in video.I

P

P

P

Progressive Mesh

MPEG1

B

B

B

Property 1

I

P

P

P B

B

B

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Retransmission is Needed

One packet loss may disable the decoding of many subsequent vertex splits.

Retransmission is important.

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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

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importance

Vertex splits

Property 2

The importance of vertex splits decreases quickly.

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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.

packet 1 is lost

packet 1 is retransmitted

time

quality

Case 2

Case 1

Case1: all following packets dependent on the lost packet Case2: all following packets are independent.

19time

quality

Quality Curve

Objective is to improve the quality on the client side.

The quality changes with time.

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time

quality

Our Objective

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

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quality

time0

tDv

wv

Decoded Mesh Quality

Area under the curve

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The Key is Dv

Dv is a random variable since packet loss is random.

Need to find E[Dv] for each vertex split.

Dv depends on Loss rate (channel property) Dependencies among data (data

property)

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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

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Td

Td

Si

Assumptions

UDP + retransmission Constant sending rate We Retransmit lost

packet as soon as packet loss is detected.

Packet loss is detected after time Td.

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it =i

t =i

t =0t =0

0

Time Receiver’s 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.

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Steps

Find the distribution of sending time receiving time decoding time

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Td: the time to detect packet loss

p: the loss rate

Sending Time

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

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Td

Td

Si

Si +2Td

Si +2Td

Receiving Time: Ri

Ri = Si + nTd if it is retransmitted n times.

n is a random variable with geometric distribution.

We approximate Si using E[Si].

Ri = E[Si] + nTd

The distribution of Ri can be computed.

See the paper for detail.

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Packet i Vertex v

P(v):

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

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In practice, we only consider j from Si to Si + 3Td.

Packet j received at t

Others received before t

Decoding Time: Dv

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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.

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Verification of Dv

We made two approximations: We use E[Si] to replace random variable Si in

calculating Ri. We only add up to Si + 3Td instead of infinity in

calculating E[Dv]. 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%)

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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

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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.

How much can we improve the quality if we choose a proper sending strategy?

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Worst Case vs. Ideal Case

Consider Two Extreme Cases

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Worst Case vs. Ideal Case

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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

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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.

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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

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Greedy Strategy

We can calculate Dv. gain=wv(Dv’-Dv) Pack the vertex split

with the maximum gain.

DvDv’

v

CurrentPacket

NextPacket

? ?

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gain=wv (Dv’-Dv)

importance Effect of dependency

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.

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Average Quality (Td = 40, p = 0.1)

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In 90% Cases, the quality is better than(Td = 40, p = 0.1)

45Greedy FIFO

Results

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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.

Thank You!

Q & A Time

48 FIFOaverage

Greedy90% cases

Greedyaverage

FIFO90% cases

Results