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Photo Forensics from Vanishing Points

Many forms of image tampering leave behind specific traces that can be detected. Cropping an image, however, can be hard to detect (unless the camera make/model are known and the image size can be compared against known native resolutions). At the same time, cropping can alter the interpretation of an image. For example, in 2010 a photo of an injured Israeli commando lying on the deck of a ship was published by the Reuters news agency. Reuters was accused of editorializing by cropping the original photo which showed that one of the men surrounding the commando was holding a knife. While cropping does not alter the remaining pixels, it does disrupt certain geometric properties of an image and can, under certain circumstances, be detected.

By way of backround, an image is formed when light enters a camera lens and is focused onto the sensor. The camera’s center of projection (COP) is the center of the lens, and the projection of the COP onto the image sensor is called the principle point. Because the lens is centered over the sensor, the principle point is typically near the center of the image. Significant deviations of the principle point from the image center is a tell-tale sign that the image has been cropped or modified in some other way.

In general, estimating the principle point is difficult. However, when certain combinations of vanishing lines and points are present in an image, they can be used to estimate the principle point. Shown below, for example, is an image of a box whose three visible sides are mutually perpendicular to each other.

Shown below are the vanishing lines and points for the three sides of the cube (note that I could have used different pairs of parallel lines on the cube faces and they would have yielded the same set of vanishing points).

In the figure below, I have drawn a triangle (solid red lines) whose vertices are the three vanishing points. The dashed lines are then drawn from each vertex perpendicular to the opposing triangle side. The intersection of these lines (the triangle orthocenter) is the principle point. In this case, the principle point is the image center. In general, the principle point should be at or near the image center, but can vary somewhat depending on the camera optics.

If I crop the original image so that the cube is centered, or if I edit the image by translating the cube to the far right of the image (as shown below), then the vanishing lines and points will of course remain centered on the cube and therefore be displaced to the right — something that is highly unlikely to occur naturally.

The camera principle point can be estimated from any object with three mutually perpendicular sides. The principle point should be near the center of the image and should be the same for any object from which it can be estimated. When performing this analysis, care should be taken in estimating the vanishing points, particuarly if the vanishing lines are nearly parallel. This forensic technique is limited to scenes that contain objects with three mutually perpendicular sides (a box, a dresser, a building corner, etc.), and is most useful in determining if an image has been cropped. 

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Reader Comments (1)

If the objects in the image do not have three mutually perpendicular sides, how to estimate the principle point ?

[This book is an excellent reference for different ways to estimate the principle point: Multiple View Geometry in Computer Vision (Second Edition) by Richard Hartley and Andrew Zisserman, Cambridge University Press. -Hany]

October 11, 2013 | Unregistered CommenterYan Li

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