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Filling the Joints: Completion and Recovery of Incomplete 3D Human Poses^{ †}

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## Abstract

**:**

## 1. Introduction

## 2. Literature Overview

## 3. Design of Comparative Study

#### 3.1. Matrix Completion and Recovery

#### 3.1.1. Inversion-Based Matrix Completion (IBMC)

#### 3.1.2. Gradient Descent Matrix Completion (GDMC)

#### 3.1.3. Matrix Recovery with Lagrange Multipliers (MRLM)

#### 3.2. Conducting the Experiments

#### 3.2.1. Simulated Experiments

#### 3.2.2. Real World Experiments

## 4. Results

#### 4.1. Results from Simulation Experiments

#### 4.1.1. Estimation Error as a Function of the Pose Matrix Size

#### 4.1.2. Estimation Error as a Function of Noise

#### 4.1.3. Error as a Function of the Number of Missing Joints

#### 4.1.4. Estimation Error as a Function of Time

#### 4.1.5. Estimation Error per Joint

#### 4.2. Results from Completing FHBT

#### 4.3. Runtime

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Given an incomplete pose vector (for example from a skeleton tracker) and a large database of natural human poses, we select a small subset of poses from the database based on their distance to the pose vector. This subset forms the “pose matrix”, to which we simply append the pose vector. By completing the resulting matrix, we obtain estimates for the missing joints’ locations.

**Figure 2.**A few representative frames of the MHAD dataset showing a single actor performing multiple actions such as jumping jacks, standing pikes, waving, etc. Special markers are placed at selected points on the actor’s body and his actions are recorded using multiple sensor modalities, such as RGB cameras, depth cameras, motion capture, etc.

**Figure 3.**Error as a function of the pose matrix size. We vary the size N of the pose matrix (which consists of the N closest poses selected from the pose database) and measure the resulting average error per joint, per completed pose. While GDMC and MRLM continue to improve with more evidence, IBMC exhibits a basin and becomes unstable after ~50 poses. The dashed plots represent the standard deviation of the respective techniques.

**Figure 5.**Error as a function of noise. We leave the pose database (and matrix) intact, but contaminate the to-be-completed pose vector with Gaussian noise, simulating uncertainty of real world sensors, and measure the resulting error. The x-axis shows noise standard deviation in centimeters on a logarithmic scale. Extreme noise values have been considered to showcase the performance of the algorithms in the broadest possible spectrum of noise contaminations. The dashed plots represent the standard deviation of the respective techniques.

**Figure 6.**Error as a function of the number of missing joints. The dashed plots represent the standard deviation of the respective techniques.

**Figure 7.**Error over time. We visualize the maximum error per pose produced by each of the three algorithms over a sequence of 100 temporally continuous frames. We observe a very uneven distribution of the error in the time domain, resulting in jitter in rendered sequences.

**Figure 8.**Error per joint. For each joint, we visualize a disk whose radius depends on the average expected error in estimating this joint by each of the three techniques. The skeleton belongs to a 180 cm tall man. The error disks are drawn up to this scale.

**Figure 9.**Average error and standard deviation in centimeters of FHBT extended with each of the presented matrix completion/recovery techniques compared to OpenNI and HYBRID, using the same dataset as in [7].

**Figure 10.**Average accuracy in centimeters (ratio of frames for which their average error is below a certain threshold).

**Figure 11.**Worst case accuracy in centimeters (ratio of frames for which their maximum error is below a certain threshold).

**Figure 12.**Same as Figure 9 but taking into account only the error of estimated/completed joints, respectively.

**Figure 13.**Runtime as a function of the size of the pose matrix. The y-axis shows the average time in seconds it takes to complete a single pose. Time for constructing the pose matrix is not included.

**Figure 14.**Same as Figure 13 but for pose matrices of sizes in the range 1000 to 10,000, so as to illustrate the quadratic complexity of GDMC.

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## Share and Cite

**MDPI and ACS Style**

Bautembach, D.; Oikonomidis, I.; Argyros, A.
Filling the Joints: Completion and Recovery of Incomplete 3D Human Poses. *Technologies* **2018**, *6*, 97.
https://doi.org/10.3390/technologies6040097

**AMA Style**

Bautembach D, Oikonomidis I, Argyros A.
Filling the Joints: Completion and Recovery of Incomplete 3D Human Poses. *Technologies*. 2018; 6(4):97.
https://doi.org/10.3390/technologies6040097

**Chicago/Turabian Style**

Bautembach, Dennis, Iason Oikonomidis, and Antonis Argyros.
2018. "Filling the Joints: Completion and Recovery of Incomplete 3D Human Poses" *Technologies* 6, no. 4: 97.
https://doi.org/10.3390/technologies6040097