Introduction

Active lenses are useful for two tasks [14]:

• Adaptation: Matching the camera's sensing characteristics (e.g. radiometric sensitivity, spatial resolution or focused distance) to the requirements of a given task.
• Measurement: Inferring properties of the scene by noting how the scene's image changes as the camera's parameters are varied (e.g. shape from focus).

Whether for adaptation or measurement, to effectively use adjustable lenses we need to have models of the camera's image formation process that are valid across ranges of lens settings.
However, calibrating cameras with zoom-lenses is rather difficult and raises several challenges. First, the dimensionality of data collected for calibration is large. A second challenge is the potential difficulty in taking measurements across a wide range of imaging conditions (e.g., defocus and magnification changes) that can occur over the range of zoom and focus control parameters.

The calibration problem of these cameras relies on formulating functions that describe the relationships between the camera model parameters and the lens settings. This is usually achieved by calibrating a conventional static camera model at a number of lens settings which span the lens control space using traditional calibration techniques. The calibrated model parameters at each lens setting are then stored in lookup tables [4],[10], or polynomials (or perhaps other functions) are formulated to model the parameters [7], [13],[14]. The result is a predictive camera model that can interpolate between the original sampled lens settings to produce a set of values for the terms in the static camera model for any lens setting. The approach can be summarized in:

• Collection of calibration data for fixed camera model across a range of lens settings (O₁, . . ., O_N),
• Estimation of the fixed (passive) camera model's parameter values at each lens setting,
• Characterization of the relationships between the camera model's parameters and the lens settings,
• Optimizing and refining these relationships over the whole data (global optimization).

Often polynomials are used to model the parameters variations versus lens setting [7], [13],[14], which may fail to capture complex variations in the model parameters. That is why these variations are sometimes stored in lookup tables [4],[10].

To be able to capture complex variations in the camera model parameters, we propose a complete neural framework for zoom-lens calibration. This task can be looked at as a combination of camera calibration and function interpolation over a large collection of data. Due to the proven power of neural networks as universal approximators [3], function interpolation is best attacked via MLFNs. Thus after we develop a neural network capable of calibrating the fixed parameters of a camera, we can combine it with these MLFNs into an efficient all-neural framework for the optimization of the calibration error over all data across continuous ranges of the lens control space.