# Template Matching for Wide-Baseline Panoramic Images from a Vehicle-Borne Multi-Camera Rig

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## Abstract

**:**

## 1. Introduction

## 2. Geometry of A Multi-Camera Rig System

#### 2.1. Ideal Panoramic Camera Model

**X**

_{p}, the corresponding panoramic point u with coordinate vector

**X**= [x′, y′, z′], and the panoramic center S (Figure 1a). In Equation (1),

**R**and

**T**are the rotation matrix and translation vector, respectively, and λ is the scale difference between the panoramic and world coordinate systems. In Equation (2),

**X**is restricted on the surface of a sphere with radius r.

**X**can be obtained from a 2D image point

**x**= [x, y]. In Equation (3), ϕ

_{h}and ϕ

_{v}are the horizontal angle with the range [−π, π] and the elevation angle with the range [−0.5π, 0.5π] respectively. w and h are the width and height of the panoramic image respectively. Equation (4) calculates sphere coordinate

**X**using a right-hand coordinate system.

#### 2.2. Rigorous Panoramic Camera Model

_{c}on the fish-eye image (the solid line). For convenience, the fish-eye image coordinates are usually firstly transformed to a virtual plane camera coordinates by choosing a fisheye camera model [30] and a calibration model [31]; we denote the transformation as

**K**

_{c}. Then, according to the rotation

**R**

_{c}and translation

**T**

_{c}between a fisheye camera and the virtual panoramic camera, Equation (5) describes a fisheye image point u

_{c}with a coordinate

**x**

_{c}projected to the corresponding panoramic camera point u with a coordinate

**X**.

**K**

_{c},

**R**

_{c},

**T**

_{c}are typically fixed values with pre-calibration, and k is the scale factor between the ideal plane and the panoramic sphere, which can be calculated by combining Equations (2) and (5).

**X**with its world coordinate

**X**

_{p}. According to the solid line in Figure 2b that passes C, u, and P’, a more rigorous model could be constructed as Equation (6) where the projection centre lies in the fisheye camera.

**T**

_{c}to the panoramic camera.

#### 2.3. Ideal Epipolar of Panoramic Stereo

**B**= [B

_{x}B

_{y}B

_{z}] and the corresponding rays

**X**

_{1}= [X

_{1}Y

_{1}Z

_{1}] and

**X**

_{2}= [X

_{2}Y

_{2}Z

_{2}] in panoramic coordinates.

**X**

_{2}’ =

**RX**

_{2}is the ray that has been translated to the coordinates of the left camera by a rotation

**R**. Then we have

**X**

_{1}and

**R**and a = B

_{y}Z

_{1}− B

_{z}Y

_{1}, b = B

_{z}X

_{1}− B

_{x}Z

_{1}, c = T

_{x}Y

_{1}− T

_{y}X

_{1}. Combined with Equation (2), the epipolar line of ideal panoramic stereo images is a large circle through the panoramic camera centre.

_{2}+ bY

_{2}+ cZ

_{2}= 0

## 3. Multi-View Template Matching for Panoramic Images

#### 3.1. Pre-Processing of Feature-Based Matching and Local Bundle Adjustment

#### 3.2. Error Estimation of Panoramic Epipolar

#### 3.3. Template Matching with Different Feature Descriptors

_{i}of the current candidate point i (as every point on the panoramic epipolar has its own tangent direction as shown in Figure 7b), and then obtain the direction difference between d

_{i}and the tangent direction of the reference epipolar line d

_{0}. The reference patch is rotated with d

_{0}− d

_{i}degree to compensate the angle bias (Figure 7c). The calculation of the direction difference is not very rigorous and could introduce tiny direction bias however it is very slight and could be ignored for the tremendous efficiency improvement.

## 4. Experiments and Results

#### 4.1. Test Design

#### 4.2. Results of the Wuhan Data (with Depth Map)

#### 4.3. Results of the Kashiwa Data (without Depth Map)

## 5. Discussion

#### 5.1. The Difference between the AccSIFT and SIFT Descriptors

#### 5.2. Comparison to Most Recent Studies on Template Matching

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**Some examples of image matching. (

**a**) shows the feature-based matching method that firstly extracts arbitrary features (denoted by small circles) from images and then matches them (denoted by lines); (

**b**) shows a traditional temple matching case that uses the corresponding template patch to locate four fiducial marks in an aerial image; (

**c**) shows the template matching case in our study. Given an object or patch (denoted by green box) in one image, the corresponding objects (denoted by blue box) with significant distortion should be retrieved from multi-view panoramic images.

**Figure 2.**The ideal panoramic camera (

**a**) where S, u, and p are collinear, and the multi-camera rig (

**b**) where in fact C, u, and p′ are collinear and C and S don’t overlap.

**Figure 3.**Epipolar of a panoramic image with sphere projection (yellow curve). Points in circles are selected for checking epipolar errors and bigger circles indicate larger errors (numbers beside the circles).

**Figure 4.**A virtual panoramic depth map (

**right**) generated from 3D point cloud (

**left**) using the same pose of the corresponding panoramic image (

**middle**).

**Figure 5.**Depth map supported multi-view matching. The left and right stereos are matched separately and in multi-view intersection, mistakenly matched candidates could be observed and eliminated.

**Figure 6.**The preprocessing for scale and rotation. To reduce the scale changes between stereo image patches, we can resample (

**a**) based on the ratio depth1/depth2 or resample (

**b**) based on depth2/depth1. As for rotation, both of the patch windows could be aligned to the tangent direction of the current point, as shown on (

**c**,

**d**).

**Figure 7.**The computation of the accelerated SIFT descriptor. In (

**a**), a SIFT point is described by 16 8-D vectors, which can be stored in the 16 orange points. Therefore, for every pixel in search area (

**b**) we can calculate and store the 8-D vectors only once. When a point is to be matched, its SIFT descriptor is easily retrieved. In (

**c**) the reference descriptor is rotated according to the difference of the two epipolar directions.

**Figure 9.**Performances of template matching with different descriptors on the Wuhan data. From left to right: reference image and the two adjacent search image, the results of the NCC, CENSUS, HOG, SURF and AccSIFT descriptors respectively.

**Figure 10.**Performances of template matching with different descriptors on the Kashiwa data. From left to right: reference image and the two adjacent search image, the results of the NCC, CENSUS, HOG, SURF and AccSIFT descriptors respectively.

**Figure 12.**The performances of the three template matching methods on the Wuhan data. The green box in the top images indicates the reference to be matched; the left image patches are cropped from the last frame panoramic image and the right cropped from the next frame. The results of our method are denoted by blue box; the results of DDIS-C and BBS-C are denoted by pink and red box respectively.

Total points | Minimum | Maximum | Average | <10 pixel | 10~20 | >20 pixel |
---|---|---|---|---|---|---|

76 | 0 | 35.0 | 8.29 | 53 (69.74%) | 18 (23.68%) | 5 (6.58%) |

Methods | Match Rate | Time (s) |
---|---|---|

Intensity | 72/80 | 0.202 |

CENSUS | 65/80 | 0.119 |

HOG | 69/80 | 0.344 |

SURF | 73/80 | 0.631 |

SIFT | 78/80 | 1.539 |

AccSIFT | 77/80 | 0.195 |

Methods | match Rate | Average Time(s) |
---|---|---|

Intensity | 101/120 | 1.259 |

CENSUS | 91/120 | 0.572 |

HOG | 96/120 | 1.797 |

SURF | 103/120 | 2.849 |

SIFT | 112/120 | 4.646 |

Acc SIFT | 107/120 | 1.042 |

Methods | Correct Rate | Average Time (s) |
---|---|---|

AccSIFT | 77/80 | 0.195 |

DDIS-C | 74/80 | 0.187 |

BBS-C | 63/80 | 0.325 |

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## Share and Cite

**MDPI and ACS Style**

Ji, S.; Yu, D.; Hong, Y.; Lu, M.
Template Matching for Wide-Baseline Panoramic Images from a Vehicle-Borne Multi-Camera Rig. *ISPRS Int. J. Geo-Inf.* **2018**, *7*, 236.
https://doi.org/10.3390/ijgi7070236

**AMA Style**

Ji S, Yu D, Hong Y, Lu M.
Template Matching for Wide-Baseline Panoramic Images from a Vehicle-Borne Multi-Camera Rig. *ISPRS International Journal of Geo-Information*. 2018; 7(7):236.
https://doi.org/10.3390/ijgi7070236

**Chicago/Turabian Style**

Ji, Shunping, Dawen Yu, Yong Hong, and Meng Lu.
2018. "Template Matching for Wide-Baseline Panoramic Images from a Vehicle-Borne Multi-Camera Rig" *ISPRS International Journal of Geo-Information* 7, no. 7: 236.
https://doi.org/10.3390/ijgi7070236