# Visual Information Fusion through Bayesian Inference for Adaptive Probability-Oriented Feature Matching

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## Abstract

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## 1. Introduction

- The probability framework considers the 3D global reference system, instead of a 2D image frame representation.
- A 3D probability distribution is computed and projected onto the next image, associated to the next pose of the robot, by means of a filter-motion prediction stage. Such probability projection represents relevant areas on the image, where matching detection is more probable.
- The matching process is performed in a single batch, using the entire set of feature points associated with the probability areas projected on the image, instead of a multi-scaled matching, computed feature by feature.
- The information metric permits modulating the probability values for the probability areas, instead of simply representing a set of less precise coefficients for weighting the former multi-scaled matching.

## 2. Vision System

## 3. Omnidirectional Visual Localization

#### 3.1. Angular Motion Recovery

#### 3.2. Scale Estimation

#### 3.3. Notation Definitions

## 4. Visual Information Fusion

#### 4.1. 3D Probability Distribution of Feature Existence: GP Computation and 3D Probability Sampling

#### 4.1.1. GP Computation

#### 4.1.2. 3D Probability Sampling

#### 4.2. Motion Prediction and 2D Image Projection

#### 4.3. Probability-Oriented Feature Matching

## 5. Results

#### 5.1. Matching Results

#### 5.1.1. Number of Feature Matches

#### 5.1.2. Accuracy

#### 5.1.3. Computation Time

- (a)
- feature matching;
- (b)
- matching candidates;
- (c)
- final localization estimation.

#### 5.2. Localization Results

## 6. Discussion

- Adaptive probability-oriented feature matching.
- Stable amount and accurate matches provided, in contrast to standard techniques.
- Efficient approach to work in real time.
- Robust final localization estimate in large and challenging scenarios.

## 7. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

CCD | charge-coupled device |

EKF | extended Kalman filter |

GP | Gaussian process |

GPS | global positioning system |

KL | Kullback–Leibler divergence |

MLE | maximum likelihood estimator |

SURF | speeded-up robust features |

SVD | singular value decomposition |

RMSE | root mean square error |

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**Figure 1.**Real equipment constituted by a Pioneer P3-AT robot equipped with an internal odometer, a SICK-LMS200 laser range finder, and a catadioptric vision system, namely an omnidirectional vision system. This vision system is composed of a CCD (Charge-Coupled Device) FireWire DMK21BF04 camera, assembled with a hyperbolic Eizo h Wide 70 Mirror.

**Figure 3.**Omnidirectional visual localization between poses ${\overrightarrow{x}}_{1}$ and ${\overrightarrow{x}}_{2}$. (

**a**) a 3D point $Q({x}_{Q},{y}_{Q},{z}_{Q})$ is observed from the robot reference system; (

**b**) additionally, the projections of Q, ${p}_{1}(u,v)$, and ${p}_{2}(u,v)$ are presented onto the camera reference system.

**Figure 5.**Robot navigation example in an office-like scenario along three poses: ${\overrightarrow{x}}_{n-1}$, ${\overrightarrow{x}}_{n}$, and ${\overrightarrow{x}}_{t}$. The 3D probability distribution of feature points’ existence permits associating visual feature points with a specific probability, indicated with colored spheres, whose probability values are encoded according to the left-side colorbar. Projections of a 3D point $Q({x}_{Q},{y}_{Q},{z}_{Q})$, ${p}_{n-1}(u,v)$ and ${p}_{n}(u,v)$, are also indicated. The 3D global reference system is denoted as ${S}_{global}$, and the 3D robot reference system as ${S}_{robot}$.

**Figure 7.**3D sampled probability distribution of feature existence. (

**a**) Complete 3D sampled probability distribution, $p({x}_{m},{y}_{m},{z}_{m})$; (

**b**) $p({x}_{m},{y}_{m},{z}_{m})$ evaluated at the last feature points observed (test points).

**Figure 8.**Graph diagram of a robot trajectory. Real path poses, ${\overrightarrow{x}}_{t}$, and predicted poses, ${\widehat{\overrightarrow{x}}}_{t}$, at each t are indicated, following the notation described in Equations (13) and (14). Observation measurements, ${z}_{t,n}$, and views in the environment, ${\overrightarrow{x}}_{n}$, are also depicted.

**Figure 9.**Projection of the 3D sampled probability distribution of feature existence, $p({x}_{m},{y}_{m},{z}_{m})\in $ [0.7–1], onto the image pixel axes, in t. (

**a**) 2D representation, $p({u}_{m},{v}_{m})$. (

**b**) 3D representation with Z-axis expressing probability, $p({x}_{m},{y}_{m},{z}_{m})$. (

**c**) 2D histogram representation. (

**d**) Euclidean versus polar coordinates.

**Figure 10.**Matching results between images acquired from poses at t and $t+1$. Standard matching results are indicated with blue circles, and those obtained with the proposed approach are indicated with green crosses. The pixels associated with the projected probability of feature existence $p({u}_{m},{v}_{m})$ are indicated with red dots.

**Figure 11.**Left axes: number of matches versus ${p}_{min}$. Right axes: size of the probability distribution ($log$) versus ${p}_{min}$. $-\phantom{\rule{-3.69899pt}{0ex}}\u2022\phantom{\rule{-3.69899pt}{0ex}}-$ size[$p({x}_{m},{y}_{m},{z}_{m})$]. Euclidean coordinates and distance between capture points: (

**a**) ${d}_{1}$; (

**c**) ${d}_{2}$; (

**e**) ${d}_{3}$; (

**g**) ${d}_{4}$. Polar coordinates and distance between capture points: (

**b**) ${d}_{1}$; (

**d**) ${d}_{2}$; (

**f**) ${d}_{3}$; (

**h**) ${d}_{4}$. Legend: ■ Standard matching; ■ proposed matching candidates; ■ proposed final matching.

**Figure 12.**Top row: percentage of false positives. (

**a**) Distance ${d}_{1}$; (

**b**) distance ${d}_{4}$. Bottom row: localization error (in $\beta $ and $\varphi $) versus ${p}_{min}$. (

**c**) Distance ${d}_{1}$; (

**d**) distance ${d}_{4}$. Legend: ■ standard matching; ■ proposed matching.

**Figure 13.**Computation time versus ${p}_{min}$. (

**a**) Distance ${d}_{1}$; (

**b**) distance ${d}_{4}$. Legend: ■ standard matching: matching computation; ■ standard matching: localization computation; ■ proposed matching: candidates’ computation; ■ proposed matching: matching computation; ■ proposed matching: localization computation.

**Figure 14.**Localization results in Dataset 1, $Innovatrajectory$. (

**a**) Localization estimation obtained with ground truth (black), standard matching (grey), and the proposed matching (blue); (

**b**) RMSE (m) for the localization estimation with standard matching (grey) and the proposed matching (blue).

**Figure 15.**Localization results in Dataset 2, Bovisa 10-04-2008. Localization estimation obtained with ground truth (GPS) (black), inverse EKF (red), and the proposed matching (blue).

**Figure 16.**Localization error histograms in Dataset 2, Bovisa 10-04-2008. (

**a**) Proposed approach with alignment enabled. (

**b**) Inverse EKF approach with alignment enabled. (

**c**) Proposed approach with alignment disabled. (

**d**) Inverse EKF approach with alignment disabled.

Filter-Based SLAM Stages | ||
---|---|---|

Stage | Expression | Terms |

Prediction | ${\widehat{\overrightarrow{x}}}_{t+1|t}={f}_{t}({\widehat{\overrightarrow{x}}}_{t|t},{u}_{t})$ | ${f}_{t}$: relates the odometer’s control input ${u}_{t}$ and the current state |

${\widehat{z}}_{t+1|t}={h}_{t}({\widehat{\overrightarrow{x}}}_{t+1|t},{\overrightarrow{x}}_{i})$ | ${u}_{t}$: odometer’s control input, initial prior | |

${P}_{t+1|t}=\frac{\partial {f}_{t|t}}{\partial x}{P}_{t|t}{\frac{\partial {f}_{t|t}}{\partial x}}^{T}+{W}_{t}$ | ${h}_{t}$: relates the observation ${z}_{t,n}$ and the current state | |

${P}_{t}$: uncertainty covariance | ||

${W}_{t}$: input noise covariance |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Valiente, D.; Payá, L.; Jiménez, L.M.; Sebastián, J.M.; Reinoso, Ó.
Visual Information Fusion through Bayesian Inference for Adaptive Probability-Oriented Feature Matching. *Sensors* **2018**, *18*, 2041.
https://doi.org/10.3390/s18072041

**AMA Style**

Valiente D, Payá L, Jiménez LM, Sebastián JM, Reinoso Ó.
Visual Information Fusion through Bayesian Inference for Adaptive Probability-Oriented Feature Matching. *Sensors*. 2018; 18(7):2041.
https://doi.org/10.3390/s18072041

**Chicago/Turabian Style**

Valiente, David, Luis Payá, Luis M. Jiménez, Jose M. Sebastián, and Óscar Reinoso.
2018. "Visual Information Fusion through Bayesian Inference for Adaptive Probability-Oriented Feature Matching" *Sensors* 18, no. 7: 2041.
https://doi.org/10.3390/s18072041