Next: Estimation with unknown exposure Up: .  Introduction: Variable gain image Previous: Robust statistics and yet

## Estimation with more than two input images

A simplified, though artificial situation, is when the camera is held still and the exposure is adjusted manually. Although not so realistic in today's world of mostly automatic cameras, this situation helps provide insight into the problem.

Here, a dataset of subject matter differing only in exposure, is used to calibrate the system. The sequence is from a dark interiour looking out into bright sunlight, with bright sky in the background, the dynamic range of the original subject matter being far in excess of what can be captured in any one of the constituent pictures. Such an image sequences is shown in Fig 3.

The comparagram (the square matrix that arose from (15)) is a very powerful tool for understanding the relationship between differently exposed pictures of the same subject matter since it contains all that can be known about the response function of the imaging apparatus [7]. Fig 3 shows the variable image sequence together with comparagrams for various successive pairs of images as indicated.

In this case, rather than considering all possible pairs of images in a least squares unrolling of the comparagrams, it is only necessary to consider the three possible pairs of comparagrams to get a total least squares estimate.

Reverse engineering (e.g. discovering or determining) the response function from the comparagram may be achieved through a logarithmic unrolling of the comparagram, as if it were a logistic map [2]. Applying a least squares unrolling to this data provides the recovered response function shown in Fig 4(a).

This solution recovers a lookup table, for converting an image into lightspace [7]. Although this estimate of the response function, looks reasonable, next to known points found with professional lab equipment, we can gather more insight by plotting the derivative (known as the certainty function [7]) of the response curve. This certainty function is shown in Fig 4(b).

The resulting recovered response function, , of Fig 4(a), found by unrolling the comparagrams, can be verified by regenerating ordered pairs as shown in Fig 5.

Next: Estimation with unknown exposure Up: .  Introduction: Variable gain image Previous: Robust statistics and yet
Steve Mann 2002-05-25