An efficient Error Protection Scheme for Point Based 3-D models over Packet Erasure Network

Boon-Seng Chew, Lap-Pui Chau and Kim-Hui Yap

School of Electrical & Electronic Engineering, Nanyang Technological University, Singapore, 639798

bschew@pmail.ntu.edu.sg, elpchau@ntu.edu.sg and ekhyap@ntu.edu.sg

ABSTRACT

In this paper, an efficient error protection scheme for the transmission of point based 3D model over packet erasure network is described. This scheme deals with the limitation in conventional 3D mesh model transmission where the quality of the reconstructed model is highly dependent on the lossless transmission of 3D connectivity information and the correct decoding of lower hierarchical layers of the Level of details (LOD) mesh for progressive reconstruction. The proposed scheme is particular well designed to provide connectivity and layer dependency free transmission of the static 3D model across network. Coupled with error protection technique for resilience towards packet loss during transmission, the proposed algorithm is effective in ensuring the graceful degradation of the decoded model both visually and objectively as shown from the experimental results. Key Words ⎯⎯ Channel coding, Signal processing for transmission

1. INTRODUCTION

Conventional progressive batch [3] and grain [2] refinement techniques for LOD generation of complex static 3D mesh is often paired with connectivity compression algorithm [5] to achieve data reduction and progressive reconstruction of the 3D model. The delivery of such multi-resolution model across the network is often deem as an ideal solution for reducing the latency time of previewing a highly complex model where the full downloading of the content is non-permissible in time. In the two main categories of progressive mesh, both followed a direct approach of generating a coarse base model and improving the details of the static model with added refinement packets in the form of single vertex increment or group of vertices improvement. Recently, Joint source-channel coding (JSCC) and unequal error protection (UEP) techniques [1] [7] were proposed for static LOD models in dealing with the network losses which can occur in a real-life transmission scheme. However, although both schemes are good in improving the resilience of the model during transmission, two assumptions is needed for the accurate decoding of the model namely (1) Lossless transmission of connectivity information (2) Correct decoding of the previous coarse layers. To address the two key limitations in mesh model transmission, we proposed a novel point based transmission scheme coupled with channel coding techniques to ensure the graceful degradation of 3D

model over packet erasure network. A Point based model has natural advantage over mesh model transmission as the geometries are connectivity free and decoding of LOD layers can be of non-sequential in nature. Not much researches in point based rendering have dealt with the problem of points transmission across lossy communication channels. The details of our implementation will be provided in the following section.

2. POINT BASED LOD DATA ARCHITECTURE

The data set for the points based model is define as a set of uniformly distributed N samples points over the surface of the model. { }iii zyx ,,=ρ in R3, { }Ni ,....,1∈

∞L

. Each sample can be associated with a collection of surface attributes including position, normal and texture coordinate. An approach in [9] is adopted for point based model to achieve clustering and sorting of point samples into a sequence of evenly sampled layers according to their weightage as defined by alg.1 in their respective cell. The full resolution model is then simplified into multiple layers, creating a series of of decreasing contribution to the reconstructed model. Since the different layers are not equally important, therefore an obvious way of protecting the LOD bit-stream is to add more protection to the layers that affect the quality of the quality more significant. In this paper, forward error correction (FEC) in the form of Reed-Solomon (RS) code is employed to protect the encoded bit-stream against packet losses in the network.

L ,...,, 32LL ,1

3. PACKETIZATION

Block of packet (BOP) method is adopted to packetize the different layers of LOD with their allocated channel code as shown in Fig.1. L layers of the model is generated with each having si in bytes. For the ith layer, the length is Ki and the width is wi. ST is denoted as the total source encoding bits in bytes where . Here, ∑

=

=L

iiT sS

1

α+=i

ii K

sW (1)

If the total bytes within the ith layer is divisible by K, α =0 else α =1 where the remaining spaces of Ki x Wi can be filled up by data from next layer. Next, FEC codes with the length of N-Ki are appended to the individual layers horizontally. Finally, each packet of M size bytes

is transmitted across the network. Here, we will like to discuss the concern of vertical assignment of packets against horizontal assignment. In the first situation, since the data bits and FEC of a single layer is assigned to the packet sequentially. It is thus a possible scenario where a single layer is no longer decodable during a burst error which results from the lost of several consecutive packets that contain information all from the same layers. In order to prevent such accumulation of errors limited within a single layer during transmission, we proposed the use of horizontal packetization within our GOP structure as shown in Fig.1. Through the proposed scheme, we can ensure that errors are evenly distributed across each layer, resulting in a higher recovery using the proposed FEC scheme. Next, we will now like to address the problem of FEC allocation to the individual layers. From the spatial dependency existing in the BOP between layers as defined in section 2, we can see that if the error occurs in the lower layers, a greater distortion is introduced to the reconstructed model. Therefore, in order to minimize the effect of the transmission error, an appropriate allocation of channel protection bits is necessary when the global transmission rate is constant throughout a BOP. Below, we will discuss the channel bits allocation scheme and state the optimization process performed. 4. PROPOSED CHANNEL ALLOCATION SCHEME

The overall bit budget is defined as Q in this paper. Q represents the maximum allowable source and channel bits used to represent the model. Here, we vary the Bpv (bits per vertex) parameter for simulating the dynamical nature of the channel. Since the size of the different layer of source information does not change during transmission for a similar model. The problem that remains is to find the optimal channel allocation for the different layers of source

information given a variation in the channel bandwidth. We state the objective of the optimization function as finding the minimum distortion upon channel allocation for the individual layers such that the total bit budget should not exceed N x M where N is the total numbers of packets to be transmitted and M as the packet sizes (bytes) for each single packet. In this paper, we assume the packet size to be fixed for each packet. The channel bits allocation to the individual layers is denoted as where it is proven in [11] that the channel rate should always follow the characteristic of non-decreasing nature for optimal allocation. denotes the channel rate for the ith layers of the BOP. The non-decreasing channel rate characteristic defines a higher allocation of channel bits to the more important lower layers. The earlier constraint ensure that the overall bit rate does not exceed Q while minimizing the overall expected distortion for the bit-stream. The resultant distortion of the model is defined in (2). represents the initial distortion with the base layer decoded and

Lrrrr ...321 ≥≥≥

1r

)( 11 rDΔ

)( ll rDΔ denotes the following distortion reduction upon receiving the enhancement layer at the decoder end.

   

Layer1

Layer2

Layer3

…………….

Layer L

M Packet size

……

……

……

……

……

……

……

……

……

……

……

……

…

K1

N-K1

KL

N-KL

FEC

FEC

FEC FEC

FEC Packet 1

Packet N

Fig.1. Packetization scheme for UEP allocation

)()()()~(2

11 l

L

lll rPrDrDrD ×Δ+Δ= ∑

=

(2)

Two state Markov model is applied here as the channel estimator for it accuracy and extensive usage in multiple literature for channel loss estimation. The probability can be calculated by P (m,N) which illustrates the probability of losing m packets within N packets. As long as the number of lost packets doesn’t exceed the number of protection packets, the original data can be reconstructed. We formulate the probability as follow: )( lbP

(3) =)( lbPN

∑−

=

K

mNmP

0),(

Lastly, we need to determine the distortion parameter in the optimization problem. In this paper, a distortion metric suitable for measuring mean variation of point based model is proposed. Comparing our method to the conventional method in [6], Hausdorff distance is commonly used for finding the maximum differences between two different mesh models. Our method is more inclined towards determining the mean variation between the individual points of the two models, thus giving us a better accuracy in this case for determining the overall error between two point based models upon transmission. We defined the proposed error metric in the following section.

5. PROPOSED ERROR METRIC

For each vertex i belonging to model X, the minimal distance to the model X’ can be defined as: iXD ,

)min(1

,',' ∑=

∀→ −=n

ikXiXkXX BBD (4)

||.|| of (4) denotes the commonly used Euclidean norm where the maximum Euclidean distance obtained will be taken as the one sided Hausdorff distance of X and X’. denotes the total distortion contributed by each point within a point based model. Thus, the differential improvement of each layer i can be determined and we can proceed to solve the optimization problem. The result from the simulation will be presented in the next section

'XXD →

6. EXPERIMENTAL RESULT

We have proposed an unequal error protection scheme for points based 3D model suited for transmission in lossy channel in this paper. In earlier section, we present the problem formulation in understanding the channel bit allocation for the individual layer. Using the optimization algorithm, we are able to determine the best possible channel rate allocation to the individual layers giving unequal error protection to each layer according to their importance during reconstruction. In this section, we conduct experiment in our proposed technique for several point based 3D models and present the result for the “horse” model here. The horse model is made up of 100000 point clouds vertices data. It can be observed that more vertices are commonly needed for reconstruction of 3D models in point based model comparing to mesh. Point primitive which have a smaller surface of representation, requires a larger and more distribute data set to capture the finer details of complex model. Three different error protection scheme (EEP) equal error protection, (UEP) Unequal error protection and (NEP) No error protection is adopted in the test. To ensure a fair comparison between the three schemes, the overall bit budget allocated for the transmission is fixed. The lowest priority layer in the EEP and proposed scheme will be treated as channel bits while it will be used as source bits in the NEP to ensure that additional bit that is not used as channel bit can be allocated for source encoding. The results for the horse model is shown in table 1 upon removal of similar vertices from quantization, demonstrate a common trend. The lower layers from the transmission will often introduce a distortion reduction much higher when compared to its next subsequent higher layers. It can be explained using the proposed error metrics introduced earlier in the section that enable the vertices with varying importance to be group accordingly during model reconstruction. The lower layers containing the more vital information thus result in a greater distortion reduction. The statistical result from the simulation for NEP, EEP and proposed UEP scheme is presented for discussion. We observed from Table 3 that at packet loss rate of 5%, EEP perform fairly well when compared to UEP especially in the case of

horse model where the number of vertex is large. As the packet loss ratio increases to 30%, the amount of distortion introduced by the model using EEP and NEP raised substantially. The proposed technique is able to provide the optimal protection for the model keeping the lower layers distortion low. Our method achieves a more graceful degradation of quality with increasing packet losses compare to the other two techniques. For subjective evaluation, the horse model based on the distortion measurement from the transmitted data of varying packet loss ratio (12%, 20% and 30%) is reconstructed using [8] and presented in Fig.2. Figure 2 shows the visual reconstruction of the horse model for different packet loss rating using the UEP, EEP and NEP scheme. The UEP algorithm adaptively adjust and calculate the amount of channel bits to each layers thus improving the over resilient of the data even when loss rate is increased. The proposed unequal error protection algorithm improves on this fact, giving more channel protection to the high importance layers thus increasing the error resilience of the

Table 3: Channel Allocation (bytes) for different packet loss

Horse model (Packet loss rate)

Channel allocation 5% 12% 20% 30%

Layer 1 13398 14608 15222 16289

Layer 2 5720 5577 5577 5254

Layer 3 4773 4096 4096 3810

Layer 4 3774 3364 2760 2280

Table 2: Distortion Comparison of proposed, EEP and NEP scheme

Horse model (Packet loss rate)

5% 12% 20% 30%

NEP 92.431 188.778 298.889 436.528

EEP 25.239 37.570 57.507 98.524

Proposed Scheme 25.0683 26.594 28.974 33.617

Table 1: Experimental result of horse model for LOD layers L =5, 100000 vertices, data size of 6023507 bytes

Layers Vertex Distortion Data Size

(bits)

L1 12567 61.06078 660196

L1+L2 23658 41.37089 1246607

L1+L2+L3 33728 30.977 1778611

L1+L2+L3+L4 42967 25.04399 2264692

L+L2+L2+L3+L4+L5 48080 23.61155 2530201

more detailed lower layers. This facilitates higher decodability of the more detailed model even when the variation of packet loss rate is significant thus resulting a better visual reconstruction of the model. From our experiment conducted, it is shown that using points based model during transmission enable better resilient towards the channel loss especially with a good UEP scheme. This finding is of no surprise as it displays the distinct advantage in points based model transmission when compared to mesh based. Although there is a need for more vertices to be transmitted for point based model compared to mesh, there is no direct dependency between the layers thus resulting in more decodable vertices during reconstruction. This is shown in the scenario whereby a lower detailed layer is lost during transmission; the nearby vertex position that is decodable from the other layers will inherently replace the missing vertex during reconstruction thus replacing the problem of all high batches lost as in mesh transmission.

7. CONCLUSION

In this paper, point based transmission of 3D model is proposed. Points model have a natural advantage over mesh during progressive transmission as the geometries are connectivity free and non-sequential decoding of layers is necessary. To the best of our knowledge, there is no channel rate allocation scheme proposed for point based transmission over packet erasure network. Using the proposed framework, we have shown that our method is able to provide good resilience to the 3D model during transmission with different packet lost rate simulated using a two state Markov model as the channel estimator. To measure the distortion introduce by the individual layers, an error metric for points model is suggested thus enabling optimization in computing and

allocation of unequal amount of channel protection to the individual layers based on their importance. Experimental results have shown that the proposed algorithm is effective in ensuring the graceful degradation of the decoded model both objectively and visually with different packet lost rate.

APPENDIX

Fig.2. Simulation Result of horse model for different protection scheme under varying packet loss setting model-Packet size 576, number of packets 550

REFERENCES

[1] Ghassan Al-Regib, Yucel Altunbasak, Jarek Rossignac, “An unequal error protection method for progressively transmitted 3D models,” IEEE Trans. Multimedia, vol. 7, pp. 766-776, Aug 2005.

[2] Hugues Hoppe, “Progressive meshes,” In Proceedings of ACM SIGGRAPH, 1996, pp. 99–108.

[3] Renato Pajarola, Jarek Rossignac, “Compressed Progressive Meshes,” IEEE Trans. Vis. Comput. Graph, vol. 6, pp. 79-93, Jan-Mar 2000.

[4] Miguel Sainz, Renato Pajarola, “Point-based rendering techniques,” Computers & Graphics, vol. 28, pp. 869-879, Feb 2004.

[5] J. Rossignac, “Edgebreaker: Connectivity compression for triangle meshes,” IEEE Trans. Visual. Comput. Graph. Vol. 5, pp. 47–61, Jan.1999.

[6] P. Cignoni, C. Rocchini and R. Scopigno, “Metro: Measuring Error on Simplified Surfaces,” Comput. Graph. Forum, Vol. 17(2), pp.167-174, June 1998.

[7] A. E. Mohr, E. A. Riskin, and R. E. Ladner, “Unequal loss protection: Graceful degradation of image quality over packet erasure channels through forward error correction,” IEEE J. Selected Areas in Commun., Vol.18(6), pp. 819—828, Jun 2000.

[8] M. Kazhdan, M. Bolitho, H. Hoppe, “Poisson surface reconstruction,” Eurographics Symposium on Geometry Processing, 2006, pp. 61-70.

[9] S. Zelinka and M. Garland, “Permission Grids: Practical, Error -Bounded Simplification,”ACM Trans. Graph. Vol 21(2), pp. 207-229, April 2002.

[10] T. Fang and L. P. Chau, “GOP-based channel rate allocation using genetic algorithm for scalable video streaming over error-prone networks,” IEEE Transactions on Image Processing, Vol. 15(6), pp. 1323-1330, June 2006.

[11] Cao L., “On the Unequal Error Protection for Progressive Image Transmission,” IEEE Transactions on Image Processing, Vol. 16(9) pp. 2384-88, 2007.