A comparison of different focus functions for use in autofocus algorithms

Abstract

A number of functions for the autofocusing of microscopes and other optical instruments are to be found in the literature. In this article we compare 11 of them to determine, in an objective manner, which functions are most suitable for implementation with real-time video acquisition systems. Three different images, each representing a typical class of imAutofocus algorithms are of particular importance in scanning microscope systems. The focus may have to be adjusted when the system mechanically moves from field to field, or when there is mechanical drift between two scans of the same field. In general algorithms that determine optimal focus for an image are based upon maximizing or minimizing some function that represents a "figure-of-merit." Algorithms have to be fast, as the total scan time is usually important. Thus the focus criterion functions used in the algorithms must be easy to calculate as, for example, with hardware and the video signal from a TV camera.A number of focus functions have been proposed in the literature. Some of these deal only with special applications, while others are more generally applicable. The purpose of this study is to compare different proposed focus functions and determine their domain of general or special applicability. A literature search was conducted for focus functions which could be derived from the video signal. Such functions are at a n extremum when the system is in focus. A general model for such a function is given in Figure 1 as well as some definitions of properties of the function.The following criteria are used in the selection and evaluation of the focus functions: a) Unimodality. The focus function must be unimodal; i.e., only a single maximum or minimum should be present. This simplifies considerably an autofocus algorithm and avoids potential errors from local extrema. b) Accuracy. The extremum must be present when the system is in focus. c) Reproducibility. A sharp top of the extremum results in good reproducibility. d) Range. The range over which an in-focus image can age, are used in the comparison. Among the best focus functions found in our study are the squared magnitude gradient, the squared Laplacian, and the normalized image standard deviation.

A high throughput robot system for machine vision based plant phenotype studies

“…From the work in [8,13,17,20,25], it is shown that most focus measures try to measure image properties like gray level image gradients, image contrast or frequency content. In essence they are a measure of the extent of the blur in the image.…”

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“…Therefore, autofocusing is a fundamental technology for automated micromanipulation, and its essential technique is the focus measure. A variety of spatial focus measures have been proposed (Groen et al 1985;Firestone et al 1991;Subbarao et al 1993). These three focus measures, namely normalized variance (M V ), entropy (M E ), and energy laplace (M L ), have been reported as the classic and popular focus measures.…”

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“…There is a good deal of literature on the subject of autofocus for microscopy and robotics in general (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15). Fitted with a video or digital camera and a motorized stage under computer control, the typical autofocus microscope system uses two complementary algorithms to achieve focus.…”

“…Groen et al (11) and Boddeke et al (7) established criteria for validating a focus function: it must be accurate, reproducible, computationally efficient, unimodal (having only one maximum), and of sufficient range that focus may be found from a distance. Boddeke et al (7) used a model of image formation to show that the optimal spatial filter for a focus function would sample the middle frequencies passed by the optical system.…”

“…For brightfield imaging, this focus function establishes a roughly parabolic relation between focus score and position. Acceptable focus functions have been described for brightfield (7), phase-contrast (8), and fluorescence (5,6,8) imaging, and a general method has been described (3); however, Groen et al (11) found that focus functions optimized for one imaging mode may not perform well in another. This may be particularly relevant to Nomarski-DIC because optical sectioning may resolve detail in multiple planes within a subject, potentially resulting in a multimodal focus function.…”