# Video-Based System for Automatic Measurement of Barbell Velocity in Back Squat

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Experiment Procedure Setup

- The algorithm aims to track the barbell position in the sliding plane using video images.
- A set of markers will be used to segment the barbell position.
- Once the barbell position has been located through the markers in the raster images, its position in the real world must be computed.
- Height is the only information of interest from the real-world position.
- The physical parameters relevant to this study are extracted from height measurements in each frame and video framerate.

- Section 2.2 is devoted to the fundamentals of the camera model and the proposed set-up geometry.
- Section 2.3 shows a novel method to find the sliding plane from an anterior reference plane in the structure using homography. This step is performed to find the position of the barbell markers in the real world.
- Section 2.4 deals with the automatic detection algorithm of markers from the structure reference plane.
- Section 2.5 is devoted to addressing the automatic detection algorithm of markers from the barbell.
- Section 2.6 details the extraction of the physical variables from the position of the barbell.

#### 2.2. Camera Model

_{x}and f

_{y}are the focal length in pixel units, s is the skew factor of the sensor, and (c

_{x}, c

_{y}) is the position of the principal point with respect to the upper left corner of the sensor. The origin of the 3D coordinates (X, Y, Z) is located in the optical center of the camera.

_{x}= f

_{y}. Another important aspect of the camera model is the distortion of the image due to the lens and its position in the smartphone manufacturing process. They can be modeled, respectively, as radial and tangential distortion [23,24]. We performed an analysis of several smartphone cameras with the calibration method developed in [24] and the conclusion is that these distortions are negligible.

#### 2.3. Homography

- Some marks are placed on the structural pillars of the machine to define four points: P
_{is}, with i = 1, 2, 3, 4, and associated coordinates (X_{is}, Y_{is}). Since the structural pillars are always parallel, the four points are in the same plane and therefore homography can be applied. From the quadrilateral formed by these four vertices, six distances are measured: the four sides D_{12s}, D_{23s}, D_{34s}, and D_{41s}, and the two diagonals D_{13s}and D_{24s}(Figure 3). Then, the XYZ coordinates of the four points in the Cartesian system are determined by the cosine theorem. At this stage, the reference system is placed without loss of generality, with the XY axes in the plane defined by the structural columns, so Z_{is}= 0 for i = 1, 2, 3, 4. The origin of coordinates is located at the highest and leftmost reference point P_{1s}. - In this type of gym machine, the structural columns and guide columns form two parallel planes (see Figure 1), so the distance between them is also measured as D
_{g}. - Estimate homography with reference points located in a practical place; in this experiment, in the two front structural pillars of the machine P
_{1s}, P_{2s}, P_{3s}, and P_{4s}. - With an appropriate image processing algorithm developed in the following Section 2.4, the four structural reference points are automatically located in the image as q
_{is}(x_{is}, y_{is}), i = 1, 2, 3, 4., and the homography is computed. It is defined as H_{s}since the points in the structural pillars are used. - Four points located on the guide pillars behind each reference point P
_{1s}to P_{4s}of the structural plane are defined as P_{ig}with the following corresponding coordinates: X_{ig}= X_{is}, Y_{ig}= Y_{is}, and Z_{i_g}= D_{g}, i = 1, 2, 3, 4, as shown in Figure 3b. - With the T
_{scene2cam}transformation, the q_{ig}(x, y) coordinates in the image of the points P_{ig}are computed as (x_{ig}, y_{ig}), i = 1, 2, 3, 4. - With the four corresponding pairs (X
_{ig}, Y_{ig}), (x_{ig}, y_{ig}), i = 1, 2, 3, 4, a second homography is calculated, relating the scene plane on the guide and the image plane. This homography is defined as H_{g}since the points in the guide pillars are used and are intended to map points of the image to points in the barbell plane to be able to take measurements in true magnitude. - As the camera is located on a tripod and the relative position between camera and machine does not change, the calculated homography H
_{g}is valid in all successive images of the video session. Thus, to calculate the position of the barbell during the athlete’s movement, it is enough to detect the coordinates (x, y) of the marker located on the barbell in the image, and, through homography H_{g}, the coordinates (X_{g}, Y_{g}) located on the barbell plane are obtained in true magnitude. The six distances of the markers D_{12s}, D_{23s}, D_{34s}, D_{41s}, D_{13s}, and D_{24s}and the distance to the barbell plane D_{g}are measured only once and are valid for all training sessions in that machine.

#### 2.4. Automatic Detection of Reference Points

_{s}and their automatic detection has to be robust and precise. Secondly, it is advisable to use a type of signal that a normal user can easily acquire or build. In this study, a self-adhesive warning tape is proposed as a mark signal since it meets both criteria: it can be easily placed in structural pillars and is easy to purchase at a low cost. The placement process of warning tape on the machine is not critical because only two points located in two corners of the left strip and two points in two corners of the right strip will be needed, shown as P

_{1s}to P

_{4s}in Figure 3b. The relative position between the four points can be arbitrary, as long as they are located on the same plane, and this is ensured by the construction of the machine itself, which has two parallel pillars.

- Transform the image from red, green, blue (RGB) to hue, saturation, value (HSV) colorspaces. The hue components of the red color (yellow in the case of black–yellow tape) of the warning tape and a pixel in the image are defined as hueTarget and h(x, y), respectively.
- The image DifHue(x, y) = 1–circularDif (hueTarget, h(x, y)) is calculated, where the function circularDif computes the shortest distance between the hue of the pixel and the target, going clockwise or counterclockwise along the hue scale in a circular way, 1 being the value connected to the value 0.
- To avoid the influence of pixels with low saturation, all pixels whose value in the s(x, y) component is less than 50% are set to zero in the DifHue image. This value of 50% has been selected heuristically and it is not critical.
- DifHue is binarized by selecting those colors that fall within 50% of the range between the target hue and its closest primary or secondary color. The resulting image is called DifHueBin.
- To detect the red-colored polygons, for true (white) regions in the binarized DifHueBin image, two size-based mathematical morphology tophat bandpass filters are performed [29,30,31], one with a vertical linear structuring element and another with an inclined linear structuring element at 135 degrees. Each bandpass filter is BPFilter = Tophat (DifHueBin, ee
_{1})–Tophat (DifHueBin, ee_{2}), where ee_{1}and ee_{2}are the structuring element, and their sizes, respectively, twice and half of the expected size of the polygon. Therefore, regions that are larger than twice the expected size or less than half the expected size are eliminated. This image, taken as markers, is reconstructed with the mathematical morphology reconstruction algorithm [32,33]. - To detect the left warning tape, the left half of the image is selected. The line where the polygons are located is found by adjusting a 1st degree polynomial to the upper left corner of each polygon using the random sample consensus algorithm (RANSAC) and the outliers are eliminated. The upper left corners of the highest and the lowest polygons are selected as reference points for the structural homography H
_{s}. The process is repeated on the right half of the image to detect the tape on the right and obtain its two reference points. Note that this detection process of the reference point occurs only at the beginning of the session and does not need to be updated for each image of the video if the camera is on a tripod.

#### 2.5. Automatic Detection of Barbell Markers

_{1}in Figure 5a is computed with the RANSAC algorithm. Next, a new parallel line L

_{2}(magenta), shifted to the right by half the width of the polygons, is estimated.

_{1}from the leftmost point of L

_{2}(magenta) to the line vertically dividing the image in half (blue) is taken. Finally, the left half of S

_{1}is used to search the mark, i.e., between the magenta and red lines. All pixels to the left of L

_{2}are set to zero, resulting in the ImBarbellStrip subimage. The process to detect the left barbell mark using this subimage is as follows:

- The same RGB to HSV conversion process used in the automatic detection of reference points is carried out on the ImBarbellStrip image. The calculation of DifHue = 1–circularDif (hueTarget, h (x, y)), the zeroing of the pixels with saturation less than 50%, and the same binarization performed for the detection of the pillars are also computed.
- Next, the tophat bandpass filter is again applied with a structuring element twice and half the expected size of the mark, this time with a vertical and horizontal structuring element.
- To detect the right barbell mark, the three preceding steps are repeated, but for the right part of the image. Depending on the scene, noise, glowing areas, etc., there may be no, one, or more candidates detected on each side.
- With the candidates on the left and right sides, the pair with the closest horizontal coordinate between them is selected. If a candidate is missing, it is filled in by interpolation with the images of the previous and subsequent moments.

_{g}homography is carried out only on the coordinates of the upper left corner of the marks detected on the barbell, which is a process with a computational cost much less than performing the perspective correction on all the pixels of the image.

#### 2.6. Data Analysis

_{a}is the body mass of the athlete, m

_{l}is the mass of the external load, a

_{b}is the acceleration of the barbell, and g is the acceleration due to gravity. Instantaneous power is then calculated as the product of force and barbell velocity. Mean values of these variables were computed considering the time interval required to complete the concentric range of motion of each repetition.

#### 2.7. Instrument Validation

#### 2.8. Statistical Analysis

^{2}>0.1 [1]. Finally, the validity of the two instruments was calculated with the bivariate Pearson’s product-moment correlation coefficient (r) with 95% confidence intervals (CIs), using the following thresholds: trivial (<0.1), small (0.1–0.3), moderate (0.3–0.5), high (0.5–0.7), very high (0.7–0.9), and practically perfect (>0.9) [42]. The standard error of estimate (SEE) was computed in raw units and standardized, evaluated via r to allow estimation of confidence limits [43], and interpreted using half the thresholds of the modified Cohen’s scale: trivial (<0.1), small (0.1–0.3), moderate (0.3–0.6), large (0.6–1.0), very large (1.0–2.0), and extremely large (>2.0) [42]. All statistical analyses were computed with IBM SPSS v. 22 (IBM Corp, Armonk, NY) and an available spreadsheet for validity [44].

## 3. Results

#### 3.1. Comparison between Instruments

#### 3.2. Instrument Validation

^{2}= 0.03), force (r

^{2}= 0.17), and power (r

^{2}= 0.02). As a result of the homoscedasticity of the errors, no association between the magnitude of the errors and the mean value of these variables was expected (r

^{2}< 0.1) [45,46]. The only variable showing proportional bias is the range (r

^{2}= 0.22), although the association is weak.

## 4. Discussion

^{2}< 0.1, in accordance with other studies of My Lift with peak velocity values (r

^{2}= 0.016 [17]) and other apps with mean values (r

^{2}= 0.01 [47]). Since the random error is low and stable irrespective of the velocity range measured, the proposed video system is able to detect typical small changes in velocity needed to train and monitor high-performance athletes [46].

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Experimental setup composed of a smartphone with a tripod in front of a multipower machine. Note that the structure and guide planes are parallel (dashed red lines) and that guides need to be clear to allow for a guided movement of the barbell.

**Figure 2.**Pinhole camera model used in this study. (

**a**) Direct model showing the relationships between inside and outside geometry; (

**b**) inverted model defining the geometric relationship between outside coordinates and the corresponding 2D projection onto the image plane.

**Figure 3.**Homography transformations for the measurement of the true magnitude of the barbell movement. (

**a**) Model showing the structural H

_{s}and guide H

_{g}homographies with reference points in the structural pillars P

_{1s}to P

_{4s}and guide pillars P

_{1g}to P

_{4g}, respectively. (

**b**) Location of the reference points in the multipower machine.

**Figure 4.**Automatic detection of reference points in the multipower machine. (

**a**) Original image. (

**b**) Hue, (

**c**) saturation, and (

**d**) value components of original image. (

**e**) Same image as (

**b**) but the representation of each value is in colors according to the palette hsv (

**f**) Same image as (

**e**) but all pixels with saturation lower than 0.5 are set to black. (

**g**) DifHue, taking as target the hue corresponding to the color red RGB (1, 0, 0). (

**h**) Binarized image (

**g**). (

**i**) Output of the vertical tophat bandpass filter. (

**j**) Output of the inclined tophat bandpass filter. (

**k**) Filtered image. (

**l**) Detected strip points and barbell position.

**Figure 5.**Automatic detection of the left barbell marker. (

**a**) Original image with vertical lines showing RANSAC adjustment to the bottom right corners (green); parallel line located to the right (magenta); line dividing the image in half (blue), and a line halfway between magenta and blue (red). (

**b**) Subimage selected as the portion between magenta and red. (

**c**) Hue component of (

**b**). (

**d**) 1-circularDif to the selected yellow tone. (

**e**) Image (

**d**) binarized. (

**f**) Image (

**e**) tophat bandpass filtered.

**Figure 6.**Position–time and velocity–time curves for one repetition of linear position transducer (LPT) system (blue line), video system (red line), and difference between systems (orange line); (

**a**,

**b**) 75% 1RM; (

**c**,

**d**) 85% 1RM; (

**e**,

**f**) 90% 1RM; (

**g**,

**h**) 95% 1RM.

**Figure 7.**Velocity–time curves averaged across all subjects for (

**a**) LPT system and (

**b**) video system. Blue line: 75% 1RM; red line: 85% 1RM; yellow line: 90% 1RM; purple line: 90% 1RM.

**Figure 8.**Velocity–time curves averaged across all subjects for the video system at (

**a**) 75% 1RM, (

**b**) 85% 1RM, (

**c**) 80% 1RM, and (

**d**) 95% 1RM. Velocity (red line) and absolute difference between LPT and video systems (blue line) shown with standard deviations (shaded area).

**Figure 9.**Bland–Altman plots for the measurements of LPT and video systems. Solid central line represents mean between instruments (systematic bias); upper and lower dashed lines show mean ± 1.96 SD (random error); dotted line shows linear regression (proportional bias). (

**a**) Range: regression y = –0.02x+0.41 cm, r

^{2}= 0.22; (

**b**) velocity: regression y = 0.01x–0.02 m/s, r

^{2}= 0.03; (

**c**) force: regression y = 0.04x–88.13 N, r

^{2}= 0.17; (

**d**) power: regression y = 0.01x–41.71 W, r

^{2}= 0.02.

**Figure 10.**Relationship between measurements derived from LPT and video systems. Dotted line represents linear regression; upper and lower dashed lines show 95% confidence intervals. (

**a**) Range; (

**b**) velocity; (

**c**) force; (

**d**) power. Pearson’s product-moment correlation coefficient (r) and standard error of estimate (SEE) shown with 95% confidence intervals between brackets; p < 0.01.

Range | Velocity | |

ICC (2,1) | 0.996 (0.881−0.999) | 0.988 (0.542−0.997) |

Cronbach’s α | 0.999 | 0.999 |

Mean Difference | −0.35 * (−0.39–−0.31) cm | −0.016 * (−0.018–−0.015) m/s |

SWC | 0.97 (0.87–1.09) cm | 0.02 (0.02–0.03) m/s |

SEM | 0.31 cm | 0.010 m/s |

SWC/SEM Ratio | 3.16 | 2.00 |

SEE | 0.21 (0.19–0.23) cm | 0.01 (0.01–0.01) m/s |

Standardized SEE | 0.04 (0.04–0.05) | 0.08 (0.07–0.09) |

SEE Effect Size | Trivial | Trivial |

Force | Power | |

ICC (2,1) | 0.978 (0.370−0.994) | 0.979 (0.296−0.995) |

Cronbach’s α | 0.997 | 0.998 |

Mean Difference | −15.94 * (−17.25–−14.45) N | −30.26 * (−32.78–−27.78) W |

SWC | 17.75 (15.99–19.96) N | 32.98 (29.70–37.08) W |

SEM | 13.17 N | 23.89 W |

SWC/SEM Ratio | 1.35 | 1.38 |

SEE | 8.37 (7.53–9.41) N | 15.48 (13.94–17.40) W |

Standardized SEE | 0.09 (0.08–0.11) | 0.09 (0.08–0.11) |

SEE Effect Size | Trivial | Trivial |

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## Share and Cite

**MDPI and ACS Style**

Pueo, B.; Lopez, J.J.; Mossi, J.M.; Colomer, A.; Jimenez-Olmedo, J.M.
Video-Based System for Automatic Measurement of Barbell Velocity in Back Squat. *Sensors* **2021**, *21*, 925.
https://doi.org/10.3390/s21030925

**AMA Style**

Pueo B, Lopez JJ, Mossi JM, Colomer A, Jimenez-Olmedo JM.
Video-Based System for Automatic Measurement of Barbell Velocity in Back Squat. *Sensors*. 2021; 21(3):925.
https://doi.org/10.3390/s21030925

**Chicago/Turabian Style**

Pueo, Basilio, Jose J. Lopez, Jose M. Mossi, Adrian Colomer, and Jose M. Jimenez-Olmedo.
2021. "Video-Based System for Automatic Measurement of Barbell Velocity in Back Squat" *Sensors* 21, no. 3: 925.
https://doi.org/10.3390/s21030925