Multidirectional focus measure for accurate three‐dimensional shape recovery of microscopic objects

Shape from focus (SFF) is a technique to recover the shape of an object from multiple images taken at various focus settings. Most of conventional SFF techniques compute focus value of a pixel by applying one of focus measure operators on neighboring pixels on the same image frame. However, in the optics with limited depth of field, neighboring pixels of an image have different degree of focus for curved objects, thus the computed focus value does not reflect the accurate focus level of the pixel. Ideally, an accurate focus value of a pixel needs to be measured from the neighboring pixels lying on tangential plane of the pixel in image space. In this article, a tangential plane on each pixel location (i, j) in image sensor is searched by selecting one of five candidate planes based on the assumption that the maximum variance of focus values along the optical axis is achieved from the neighborhood lying on tangential plane of the pixel (i, j). Then, a focus measure operator is applied on neighboring pixels lying on the searched plane. The experimental results on both the synthetic and real microscopic objects show the proposed method produces more accurate three‐dimensional shape in comparison to conventional SFF method that applies focus measures on original image planes. A tangential plane on each pixel in image sequence is searched by selecting one of five candidate planes. Then, a focus measure operator is applied on neighboring pixels lying on the searched plane for accurate three‐dimensional shape recovery in SFF.