The problem of binarization of gray level images acquired under nonuniform illumination is reconsidered. Yanowitz and Bruckstein proposed to use for image binarization an adaptive threshold surface, determined by interpolation of the image gray levels at points where the image gradient is high. The rationale is that high image gradient indicates probable object edges, and there the image values are between the object and the background gray levels. The threshold surface was determined by successive over-relaxation as the solution of the Laplace equation. This work proposes a different method to determine an adaptive threshold surface. In this new method, inspired by multiresolution approximation, the threshold surface is constructed with considerably lower computational complexity and is smooth, yielding faster image binarizations and better visual performance.