https://github.com/ankitdhall/vanishing-point-detector

Vanishing Point detection for images and videos using Least Squares in C++
https://github.com/ankitdhall/vanishing-point-detector

detector image-analysis image-processing least-square-regression least-squares linear-algebra regression vanishing-points vector video

Last synced: about 2 months ago
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Vanishing Point detection for images and videos using Least Squares in C++

• Host: GitHub
• URL: https://github.com/ankitdhall/vanishing-point-detector
• Owner: ankitdhall
• License: mit
• Created: 2015-08-18T06:37:30.000Z (over 9 years ago)
• Default Branch: master
• Last Pushed: 2017-07-28T13:53:09.000Z (over 7 years ago)
• Last Synced: 2024-10-31T22:32:47.099Z (about 2 months ago)
• Topics: detector, image-analysis, image-processing, least-square-regression, least-squares, linear-algebra, regression, vanishing-points, vector, video
• Language: C++
• Homepage:
• Size: 8.79 KB
• Stars: 74
• Watchers: 6
• Forks: 18
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

        
# Vanishing Point Detection using Least Squares

![](https://cloud.githubusercontent.com/assets/8938083/9835917/7c594192-5a1f-11e5-986f-5877b56e1fe6.png)  

Detector on sample footage.  

Red colored lines were considered for estimating the vanishing point. The black circle marks the region of interest, where the center of the circle is the approximate vanishing point.

1. [Dependencies](#dependencies)

2. [Speed](#speed)

3. [Algorithm](#algorithm)  

### Citing `Vanishing-Point-Detector`

Please cite our work if `Vanishing-Point-Detector` and our approach helps your research.  

```

@Misc{Vanishing-Point-Detector,

  author = {{Dhall*}, A. and {Chandak*} Y.}

  title = "{Vanishing Point Detection using Least Squares}",

  howpublished = {\url{https://github.com/ankitdhall/Vanishing-Point-Detector}},

  year = {2015}

}

```

## Dependencies

* OpenCV for C++

* Armadillo

## Speed

Average performance: 21 fps

## Algorithm

* The algorithm starts by computing `dx` and `dy` of the image.

Then the edge vectors are formed which encodes the direction

and magnitude at each pixel.  

* This field is segmented into connected regions of pixels that

share the same vector direction up to a certain tolerance.  

* The principal axis of the bounding box enclosing this region

gives a single pixel thick straight line. Then, `x`, `y` co-ordinates of

either ends are stored.  

* Then the lines are converted to the `ax + by = c` form.  

* These co-efficients `(a, b, c)` are stored in the matrix `A`, `B` in the

following format:  

```

     A = [a1 b1  

          a2 b2  

            ..  

            ..  

         an bn]    

     B = [c1 c2 ... cn ]'  

```

* Solve for vector `X` in `AX = B` with the concept of least

square approximation of the answer. Where `X = [x y] T`

* For each pair of lines in the matrix A, their point of intersection

`X’ = [x y] T` is found. This is multiplied with the matrix `A` and

then `B` is subtracted to get the error vector `E`.

```

    E = AX’ – B

```

* The squared sum of error vector is computed and whichever

`X’` gave the least summation of errors is chosen as the

vanishing point in the image.