# Detection and Classification of Artifact Distortions in Optical Motion Capture Sequences

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## Abstract

**:**

## 1. Introduction

## 2. Background

#### 2.1. Sources and Types of Distortions

- 1.
- Simple gap—appears when reconstruction algorithms give up, it is the least type of concern (a trivial case);
- 2.
- Single peak—caused by transient erroneous marker matching techniques. It is simple to detect;
- 3.
- Heavy noise of a much larger amplitude than ordinary noise introduced by frequent erroneous marker matching techniques;
- 4.
- Rectangular distortion—forward (followed by backward) steps caused by mismatching the 3D positions of the markers (part of the 3D trajectory is assigned to another marker) or due to the erroneous marker reconstruction based on a rigid body model;
- 5.
- Slow value change—two potential sources—accumulated reconstruction errors in successive frames (e.g., when there is deformation of a body, which is the failure of a commonly assumed rigid body model) or the result of low-pass filtering of peaks.

#### 2.2. Previous Work

## 3. The Proposal

#### 3.1. Premises—Correlation of Trajectory Coordinates

#### 3.2. The Method Overview

#### 3.3. Regressive Models

#### 3.3.1. Savitzky–Golay Filter

#### 3.3.2. Neighbor-Based Linear Least Squares Loose Model

#### 3.3.3. Regression with Neural Network

#### 3.4. Recognition and Classification of Distortions

#### 3.4.1. Locating Sudden Changes

`find_derivate_pairs(dX,T,maxlen)`), which looked for opponent differential pairs

`dX`, exceeded the threshold level

`T`, and was no more distant than some presumed maximal length

`maxlen`. It results=ed in binary decision variables marking located ranges. The function parameters—threshold and distance—depend on the data characteristics and sampling frequency.

#### 3.4.2. Identifying Single Peaks

- $window$—for the moving average, we assumed it to be 19 samples long;
- $threshol{d}_{1}$—it is calculated statistically from the data using ${k}_{1}\xb7\sigma $ of ${D}_{HP}$—w employed $3\xb7\sigma $ as a default value; however, any ${k}_{1}$ can be provided as the parameter;
- $threshol{d}_{2}$—(anti-sensitivity) for the $ampRatio$;
- $maxSize$—(default 5), which declares the maximal size of the expected peaks; it affects the size of moving sum windows ${W}_{n}$, which is $2\xb7maxSize+3$ samples long, it also defines the size of the linear structuring element for morphological operations S.

#### 3.4.3. Heavy Noise

- $threshold$—this is calculated statistically from the data using ${k}_{2}\xb7\sigma $ of ${D}_{HP}$—w employed $2\xb7\sigma $ as a default value; however, any k can be provided as parameter;
- Minimal length of the segment ($minLen$), which is used to define the linear structuring element S as $2\xb7minLen-1$; we assumed $minLen=20$ samples;
- Default parameters of Savitzky–Golay are L = 5, M = 13.

#### 3.4.4. Step Change

`find_derivate_pairs`, which seeks the areas between the complementary pairs of differential peaks (above $threshold$); we interpret it as a rectangular distortion, as shown in Figure 11. This scanning requires setting up two parameters—$minLen$ and $maxDist$, identifying the minimal length of a step change, and maximal distance of searching.

- $threshold$—this is calculated statistically from ${D}_{HP}$ using ${k}_{3}\xb7\sigma $ of—we employed $3\xb7\sigma $ as a default value; however, any ${k}_{3}$ can be provided as parameter,
- Minimal length of the segment ($minLen$); we assumed $minLen=20$ samples;
- Maximal searching distance $maxDist$; we assumed 200 samples as the default value.
- Default parameters of Savitzky–Golay are the same as for heavy noise L = 5, M = 13.

#### 3.4.5. Identifying Slow Changes

- 1.
- Smoothed the R with the Savitzky–Golay low-pass filter (L = 7, M = 11—parameters heuristically tuned).
- 2.
- The upper threshold ${T}_{u}$ was set up with a ${k}_{U}\xb7\sigma $ rule of a thumb—in our case, three times ${\sigma}_{R}$ was selected (${k}_{U}=3$) as the default would identify the significant tops and bottoms of the hills and valleys.
- 3.
- If the top or bottom lengths were shorter than some minimal ${\tau}_{U}$, we skipped it (0.2 s—20 frames in our case), assuming it to be short-term fluctuation.
- 4.
- After the identification of a top/bottom value, we looked for the rest of a distortion (below threshold)—the marked range expanded both sides iteratively (in the past and future) until the residual value went below/above the lower threshold ${T}_{L}$, obtained with ${k}_{hv}\xb7{\sigma}_{R}$ with ${k}_{hv}=0.5$ as the default value.
- 5.
- If the overall located distortion (hill/valley) was shorter than some value ${\tau}_{hv}$ (50 frames—0.5 s), it was omitted, as one can consider it a short-term fluctuation of the predictor.

## 4. Verification of the Method

#### 4.1. Materials and Methods

#### 4.1.1. The Data

#### 4.1.2. Experimental Protocols

#### 4.1.3. Artifact Contamination Procedure

- The sign was a +1/−1 value drawn with equal probabilities;
- The amplitude was a Gaussian random variable with assumed amplitude and standard deviation (in the tested cases: $\mu =5\phantom{\rule{0.166667em}{0ex}}\mathrm{or}\phantom{\rule{0.166667em}{0ex}}10$ mm and $\sigma =0.4\xb7\mu $); these values were used to scale the peak of the rectangle or triangle distortion and as the standard deviations in the heavy noise area;
- Distortion durations and intervals were part of the Poisson process; an average length of distortion was set up to 50 samples, and the interval length was adjusted according to the duration of the sequence and the target amount of the given distortion.

#### 4.2. Results and Discussion

#### 4.2.1. Synthetic Distortion Classification

- The clear signal was identified properly for more than 99% of samples; a negligibly small amount of distorted samples was erroneously identified as clean signals (compared to the overall cardinality of the class).
- For the peak change, sensitivity was approximately 66% and 90%, and the main misclassification was in a clear signal; this class was not a cause of confusion for the other classes compared to a clean signal (usually below $FPR=50\%$).
- Heavy noise sensitivity was above 88%; the main confusions were step change and a clear signal; this class was rarely erroneously recognized in place of the others ($FPR$ = 4–8%); the main confused class was a clear signal.
- For the step change, sensitivity was approximately 70% and the main confusion was slow change; this class was erroneously recognized in place of others at a moderate rate ($FPR$ = 12–27%)—here, a clean signal and heavy noise were wrongly identified.
- For the slow change, $TPR$ was a bit more than 50% and the main confusion was a clear signal; this class was often difficult and erroneously recognized in place of others ($FPR$ = 80–90%)—usually, it was a clear signal, but a step change and heavy noise were also wrongly identified.

#### 4.2.2. Comparing to Human Operators

#### 4.2.3. Applicability Testing

- Peak changes were effectively removed with interpolation methods—simple linear or spline (piecewise cubic polynomial); the other two methods in perfect detection would not offer even comparable efficiency, yet in actual classification, they offered just slightly worse performances.
- FFNN offered the best performance for all ‘bulky’ distortions (of longer durations), both hypothetical and classified cases.
- Heavy noise, aside from FFNN, was well cleaned with the Savitzky–Golay filter (see Figure 17b).
- Step changes could be effectively removed with FFNN only.
- Slow changes were the most contradictory—the only appropriate reconstruction method was FFNN; in the case of perfect detection, the efficiency was high, but due to the limited actual detection, the results were quite poor. These results correspond well to the detection of slow changes in E1—low sensitivity and high fall out.

#### 4.3. Results Recap

## 5. Summary

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

FFNN | feed-forward neural network |

HF | Hampel filter |

HML | Human Motion Laboratory |

LS | least squares |

M3S | moving three sigma |

mocap | MOtion CAPture |

MSE | mean square error |

NARX-NN | nonlinear autoregressive exogenous neural network |

NN | neural network |

PJAIT | Polish–Japanese Academy of Information Technology |

RMSE | root mean squared error |

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**Figure 1.**Processing in the early stages of the motion capture pipeline with distortion sources (red) and problems to solve (yellow), question marks (?) indicate ambiguous choices.

**Figure 2.**Identified types of distortions inpainted into exemplary data—the first coordinate of the first marker (head) of the IM subject.

**Figure 3.**Correlation between X position of markers in exemplary sequence (fast walking HJ subject): (

**a**) the whole sequence, all 53 markers; (

**b**) inter-marker correlation function for the selected correlated and non-correlated markers.

**Figure 5.**Outline of the body model, with body parts distinguished with individual random colors and underlying skeleton included (

**a**), and corresponding parts hierarchy annotated with parents and siblings (

**b**).

**Figure 6.**Performance of the two predictor models of ${P}_{3}^{4}$ (with and without former values of the predicted variables): (

**a**) first dimension of the first marker (with artificial distortions); (

**b**) residual histograms and corresponding Laplace PDFs for ${R}_{3}^{4}$ (for explanation of the model construction and parameters, see Equation (8)).

**Figure 7.**Predictor parameter tuning with preliminary data for three subjects, quality as standard deviation averaged over all markers; the tuned parameters: L—polynomial order, k—context size (lags).

**Figure 9.**Actual distortion prediction and residuals—component (${R}_{m}$) and final (R), compared with the polynomial residual ${R}_{9}^{1}$.

**Figure 11.**Appearance of sudden distortions in residual/high-pass ($R\left(n\right)$)—single peak and step change, and their corresponding peak pairs in differential $D\left(n\right)$.

**Figure 12.**Slow detection: (

**a**) original, predicted, and distorted signal, (

**b**) residual with hysteresis thresholding.

**Figure 13.**Average confusion matrix for detection of synthetic noises for a 1000-fold simulation with 5-mm average amplitudes of distortions and shares: (

**a**) 5%, (

**b**) 10%, (

**c**) 20% of time (blue—successful results, red—faulty).

**Figure 14.**Average confusion matrix for detection of synthetic noises for a 1000-fold simulation with 10-mm average amplitudes of distortions and shares: (

**a**) 5%, (

**b**) 10%, (

**c**) 20% of time (blue—successful results, red—faulty).

**Figure 15.**Averaged confusion matrix for detection with M3S (

**a**–

**d**) and the Hampel filer (

**e**–

**h**) of synthetic anomalies for a 1000-fold simulation with 10-mm average amplitudes of distortions and a share 20% of the time (blue—successful results, red—faulty).

**Figure 17.**Artifacts and the removal with methods tested in E3: (

**a**) single peaks, (

**b**) heavy noise, (

**c**) step change, (

**d**) slow change. Please mind the various scales in the axes.

No. | Name | Scenario | Duration | Difficulty |
---|---|---|---|---|

1 | Static | Actor stands in the T-pose in the middle of the scene, looks around, and shifts from one foot to another | 22 s | easy, static |

2 | Sitting | Actor stands in the middle of the scene and then sits on a chair; actor stands again after a few seconds and repeats this three times | 29 s | occlusions |

**Table 2.**Comparing the number of distortions located by the proposed method to the human operator (E2).

Operator | Seq. No | Recording | Errors Identified by | Error Verification | |||
---|---|---|---|---|---|---|---|

Human | Algorithm | Approved | Rejected | Missed | |||

None | 2 | Sitting | — | 29 | 16 | 13 | 4 |

Expert | 2 | Sitting | 20 | 9 | 0 | 0 | 0 |

Intermediate | 2 | Sitting | 18 | 11 | 2 | 9 | 0 |

Beginner 1 | 2 | Sitting | 10 | 37 | 20 | 17 | 2 |

Beginner 2 | 2 | Sitting | 11 | 46 | 26 | 20 | 1 |

**Table 3.**$RMSE$ after reconstruction with different methods (with perfect and algorithmic artifact classifications) for the mocap sequence with a 5% distorted time in the sequence.

Peaks | Heavy Noise | Step Change | Slow Change | |
---|---|---|---|---|

Distorted | 0.19065 | 0.17717 | 0.18069 | 0.10129 |

Linear interpolation (perfect) | 0.00136 | 0.18322 | 0.15939 | 0.18795 |

Linear interpolation (classified) | 0.03947 | 0.18514 | 0.15623 | 0.29339 |

Savitzky–Golay filter (perfect) | 0.01900 | 0.04963 | 0.17440 | 0.10130 |

Savitzky–Golay filter (classified) | 0.08159 | 0.06855 | 0.17553 | 0.10173 |

Spline interpolation (perfect) | 0.00025 | 0.11041 | 0.09780 | 0.10972 |

Spline interpolation (classified) | 0.03429 | 0.68692 | 0.10895 | 0.19935 |

FFNN predictor (perfect) | 0.01841 | 0.01953 | 0.01933 | 0.01875 |

FFNN predictor (classified) | 0.03944 | 0.04547 | 0.04409 | 0.11000 |

**Table 4.**$RMSE$ after reconstruction with different methods (with perfect and algorithmic artifact classifications) for the mocap sequence with a 10% distorted time in the sequence.

Peaks | Heavy Noise | Step Change | Slow Change | |
---|---|---|---|---|

Distorted | 0.26906 | 0.26340 | 0.26282 | 0.15037 |

Linear interpolation (perfect) | 0.00186 | 0.25487 | 0.28409 | 0.27662 |

Linear interpolation (classified) | 0.05144 | 0.26360 | 0.27618 | 0.38908 |

Savitzky–Golay filter (perfect) | 0.02678 | 0.07211 | 0.25361 | 0.15046 |

Savitzky–Golay filter (classified) | 0.08959 | 0.08895 | 0.25510 | 0.15083 |

Spline interpolation (perfect) | 0.00039 | 0.14679 | 0.15207 | 0.15955 |

Spline interpolation (classified) | 0.04754 | 0.95512 | 0.16358 | 0.23918 |

FFNN predictor (perfect) | 0.02785 | 0.02468 | 0.02581 | 0.02612 |

FFNN predictor (classified) | 0.05537 | 0.05201 | 0.06349 | 0.14717 |

**Table 5.**$RMSE$ after reconstruction with different methods (with perfect and algorithmic artifact classifications) for the mocap sequence with a 20% distorted time in the sequence.

Peaks | Heavy Noise | Step Change | Slow Change | |
---|---|---|---|---|

Distorted | 0.38228 | 0.39623 | 0.39247 | 0.21676 |

Linear interpolation (perfect) | 0.00273 | 0.44107 | 0.44015 | 0.39172 |

Linear interpolation (classified) | 0.07007 | 0.45679 | 0.45630 | 0.55692 |

Savitzky–Golay filter (perfect) | 0.03880 | 0.11228 | 0.37892 | 0.21704 |

Savitzky–Golay filter (classified) | 0.10383 | 0.16007 | 0.38120 | 0.21748 |

Spline interpolation (perfect) | 0.00058 | 0.24337 | 0.28188 | 0.25274 |

Spline interpolation (classified) | 0.06753 | 1.58979 | 0.37534 | 0.35679 |

FFNN predictor (perfect) | 0.04169 | 0.03711 | 0.03972 | 0.03735 |

FFNN predictor (classified) | 0.07903 | 0.11433 | 0.10284 | 0.20549 |

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Skurowski, P.; Pawlyta, M.
Detection and Classification of Artifact Distortions in Optical Motion Capture Sequences. *Sensors* **2022**, *22*, 4076.
https://doi.org/10.3390/s22114076

**AMA Style**

Skurowski P, Pawlyta M.
Detection and Classification of Artifact Distortions in Optical Motion Capture Sequences. *Sensors*. 2022; 22(11):4076.
https://doi.org/10.3390/s22114076

**Chicago/Turabian Style**

Skurowski, Przemysław, and Magdalena Pawlyta.
2022. "Detection and Classification of Artifact Distortions in Optical Motion Capture Sequences" *Sensors* 22, no. 11: 4076.
https://doi.org/10.3390/s22114076