# Correcting Scale After Perspective Adjustment

Correcting Scale After Perspective Adjustment

Thursday 26th December 2013 11:51pm

## Introduction

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This can be used to good dramatic effect, but usually it is an unwanted side-effect of the camera to subject geometry. By stretching the top of the image (using, say, the perspective adjustment transformation in PhotoShop) the verticals can be restored.

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Obviously this 'foreshortening' effect is more readily apparent with some subjects than others. It is nevertheless worth understanding the effect so that the image's deviation from reality is under the control of the photographer, not the equipment.

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This final version of the street scene has been vertically stretched by 35%, but without obvious reference points (such as circles and squares) how can we know after the fact what the appropriate proportions are. We can achieve something aesthetically pleasing 'by eye' but minor geometric errors can leave an image somewhat disquieting. Fine photography often relies on the cumulative effect of many, individually indiscernible, tweaks. Relying on adjustments judged 'by eye' alone risks sacrificing the final image quality.

So here, I am investigating the relationship between the degree of perspective correction and the degree of stretch the resulting image requires.

## Investigation

For this investigation I need a subject of known geometry, so I drew up a shooting target consisting of a grid of 2.5cm squares with a large circle overlaid. This I placed almost parallel to a camera sensor and I took a series of shots at increasing angles of recline. ×

I then followed the following method for each of the 8 shots.

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*Tan(A) = opposite/adjacent*

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The following table shows the measured relationship between angle of perspective adjustment and required scaling:

Angle Of Adjustment | Scaling Factor |

1.9 | 1.03 |

3.1 | 1.1 |

5 | 1.22 |

6 | 1.3 |

7.4 | 1.42 |

9.7 | 1.67 |

12 | 1.97 |

26.3 | 4.55 |

A least squares regression (LINEST function in Excel) determines a straight line fit for this data of:

*Scaling Factor = 0.092 * Angle + 0.793*

Or perhaps more readily helpful, although less accurate:

*Scaling Factor = (Angle + 8)/10*

## Conclusions

For perspective adjustments of three degrees or more the foreshortening effect is significant.For adjustments of more than eight degrees the foreshortening is severe. Total recovery may not be advisable as interpolation effects will degrade the final image significantly.

Images that contain objects that have readily recognisable proportions (standard doors, windows, people for example) will suffer from perspective adjustments that are not consequently scaled in the appropriate direction.