• autofocusing;
  • focus measurement;
  • human brightness perception;
  • logarithmic image processing (LIP);
  • microscopy;
  • shape-from-focus


The logarithmic image processing (LIP) model is a mathematical framework which provides algebraic and functional operations for the processing of intensity images valued in a bounded range. The LIP model has been proved to be physically consistent, most notably with some image formation models and several laws and characteristics of human brightness perception. This paper addresses the image focus measurement problem using the LIP model. The three most classical image focus measurements: the sum-modified-Laplacian, the tenengrad and the variance, which aim at estimating the degree of focus of an acquired image by emphasizing and quantifying its sharpness information, are considered and reinterpreted using the LIP framework. These reinterpretations notably make attempts at evaluating degrees of focus in terms of human brightness (sensation) from physical light stimuli. Their potential is illustrated and validated on shape-from-focus issues on both simulated data and real acquisitions in digital optical microscopy. The concept of shape-from-focus involves recovering the shape of an observed thick sample by locally maximizing a focus measurement throughout a sequence of differently focused images. Finally, it is shown that the LIP-based focus measurements clearly outperform their respective classical ones.