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Using Vanishing Points to Correct Camera Rotation. Andrew C. Gallagher Eastman Kodak Company andrew.gallagher@kodak.com. Problem. An unintentionally tilted camera can negatively affect image appearance. Caused by lightweight cameras that are difficult to hold level.

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using vanishing points to correct camera rotation

Using Vanishing Points toCorrect Camera Rotation

Andrew C. Gallagher

Eastman Kodak Company

andrew.gallagher@kodak.com

Andrew C. Gallagher 1

CRV2005

problem
Problem
  • An unintentionally tilted camera can negatively affect image appearance.
  • Caused by lightweight cameras that are difficult to hold level.
  • People prefer imageswhere the horizon is level.
  • Human can see as little at 1o tilt.

Andrew C. Gallagher 2

CRV2005

solution
Solution
  • Vanishing point location can be used to detect and correct image tilt resulting from camera rotation.
  • A vanishing point is the image of a world line at infinity.
  • Vanishing point location is useful for:
    • computing focal length [Kanatani]
    • finding principal point [Caprile et al.]
    • determining camera parameters and rotation matrix[Cipolla et al.]

Andrew C. Gallagher 3

CRV2005

vanishing points
Vanishing Points
  • Parallel scene lines meet at a vanishing point in the image.

Vertical Line

Vanishing Point

Horizontal Line

Vanishing Point

Andrew C. Gallagher 4

CRV2005

the camera model
The Camera Model
  • The camera model describes the projection of 3D world to 2D camera plane.
  • K is a 3x3 matrix of the internal camera parameters.
  • R is a 3x3 matrix describing the rotation from the world to the camera frame.
  • T is a 3x1 matrix describingtranslation between the world and camera coordinate frame.
  • Assume no skew, square pixels. The vanishing points of world directions are:

world

coordinate frame

camera

coordinate frame

Andrew C. Gallagher 5

CRV2005

the rotation matrix
The Rotation Matrix
  • R is any matrix in the special orthogonal group SO(3).
  • In practice the camera positions used by typical consumers follow a fairly predictable nonlinear distribution.
  • This distribution is then used to find where vanishing points will occur.

Andrew C. Gallagher 6

CRV2005

camera position analysis
Camera Position Analysis

World rotation by qabout the Y-axis

Default Position

World rotation by f about the X-axis

World rotation about the Z-axisTILTED IMAGE

Andrew C. Gallagher 7

CRV2005

camera position analysis8
Camera Position Analysis
  • This position model encompasses all “preferred” camera positions.
  • The vanishing point associated with vertical world direction (Y-axis) is constrained to fall on the image y-axis.
  • The horizon is parallel to image x-axis.

Rotation about both X- and Y- axes

Location of Vy

Location of Vx or Vz

Andrew C. Gallagher 8

CRV2005

camera position analysis9
Camera Position Analysis
  • The original rotation matrix is multiplied by a rotation about the Z-axis.
  • The new vanishing points are simply rotated by the same amount!
  • In essence, the rotation of the camera from the ideal position is equivalent to the rotation of the vanishing points.

Additional rotation about the Z-axis

Location of Vy

Location of Vx or Vz

Andrew C. Gallagher 9

CRV2005

ground truth analysis
Ground Truth Analysis
  • 357 vanishing points were manually labeled to compare with expected distribution.
  • 160 vertical (Vy) vanishing points197 horizontal (Vx or Vz) vanishing points.
  • The match is visually good.

Location of Vy

Location of Vx or Vz

EXPECTED DISTRIBUTION

MEASURED DISTRIBUTION

Andrew C. Gallagher 10

CRV2005

vanishing point classification
Vanishing Point Classification
  • The vertical and horizontal vanishing point distributions are well-separated.
  • A classifier can be used to identify vertical vanishing points.
  • The camera rotation is found from the vertical vanishing point.
  • On ground truth, only 2vanishing points (0.6%)are misclassified.

Vertical vanishing point

classifier

Andrew C. Gallagher 11

CRV2005

the tilt correction algorithm
The Tilt Correction Algorithm
  • Find vanishing points
  • Identify vertical vanishing points
  • Compute camera rotation angle b from the vertical vanishing point
  • Compute correction angle bc according to table:
  • Rotate image
  • The rotated image can beshown to be equivalent to capturing with a camerahaving no componentof rotation about the Z-axis.

^

Andrew C. Gallagher 12

CRV2005

vanishing point detection
Vanishing Point Detection
  • Initial work by Barnard 1983.
  • Line Segment Detection
    • Lines are found by calculating local gradients, then clustering, or by using Hough transform.
  • Line Intersection Computation
    • Intersections of the lines are found. Line intersections are possible locations of a vanishing point.
  • Maximum Detection
    • A detected vanishing point is hypothesized to be at a location of many line intersections.

Andrew C. Gallagher 13

CRV2005

vanishing point detection14
Vanishing Point Detection

Lines associated with 1st VP.

Original Image

Plot of all line segment

Intersections (Higher

probabilities are red).

Detected Vanishing

Points

Lines associated with 2nd VP.

Detected Line Segments

Andrew C. Gallagher 14

CRV2005

algorithm results

Lines associated

with vertical VP

Algorithm Results

Original

Corrected

Andrew C. Gallagher 15

CRV2005

algorithm results16

Lines associated

with vertical VP

Algorithm Results

Original

Corrected

Andrew C. Gallagher 16

CRV2005

conclusions
Conclusions
  • Rotation of the camera about the principal axis moves the vertical vanishing point from the image y-axis.
  • This novel algorithm corrects a tilted image by detecting the vertical vanishing point, and determining the magnitude of camera rotation.

Andrew C. Gallagher 17

CRV2005