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ONE-IMAGE DEPTH-FROM-FOCUS FOR CONCENTRATION 
MEASUREMENTS 
Peter Geißler 
Interdisciplinary Center for Scientific Computing, University of Heidelberg 
Im Neuenheimer Feld 368, D-69120 Heidelberg, Germany 
Phone: (49) 06221-562826, email: pgeiss@davinci.iwr.uni-heidelberg.de 
Bernd Jähne 
Interdisciplinary Center for Scientific Computing, University of Heidelberg 
Im Neuenheimer Feld 368, D-69120 Heidelberg, Germany 
and 
Scripps Institution of Oceanography, Physical Oceanography Research Division 
University of California, La Jolla, CA 92093-0230, USA 
KEY WORDS: Depth-from-Focus, 3D-Point Spread Function 
ABSTRACT: 
A one-image depth-from-focus technique for the measurement of the concentration and size distribution of 
small particles is described. The technique is based on a precise knowledge of the 3-D point spread function 
and requires objects of uniform brightness and simple shapes. The true area of the object and the distance 
from the focal plane is obtained from parameters such as the apparent (blurred) area of the object and the 
mean brightness in this area. The technique has been applied to measure the size distribution of bubbles 
submerged by breaking waves. A depth criterion is used to define a virtual measuring volume that is roughly 
proportional to the size of the bubbles. 
1 INTRODUCTION 
A novel depth-from-focus technique is introduced requiring only a single image. It has been developed to 
measure the concentration and size distribution of air bubbles submerged by breaking waves into the ocean 
with an optical sensor, but it is suitable also for other particles. The measurment of bubble concentrations 
and size distributions is an important oceanographic research topic, since they influence significantly various 
small scale air sea interaction processes and wave dynamics [4] [7]. 
To measure concentrations, the number and size of the bubbles and the measuring volume have to be known. 
The measuring volume can be determined from the 3D-positions of the observed bubbles. While it is trivial 
to get the position parallel to the image plane, the position along the optical axis can be determined by the 
simple fact that the blurring in the image increases with the distance from the focal plane. Most depth- 
from-focus techniques use several images of the scene - taken with different camera adjustments. Common 
methods are depth-series [2] or multi-aperture images [3] [9]. This types of multi-image approaches cannot 
be applied to scenes with moving objects without using several cameras simultaneously. In order to solve the 
depth-from-focus problem with just one image, it is important to note that the blurred image of an object 
is given by the convolution of it is well-focused image with the point spread function of the imaging optics. 
Therefore it is not possible to distinguish whether unsharpness in an image comes from blurring or from 
object properties such as smooth brightness changes. A priori knowledge of the point spread function and 
the properties of the observed objects is therefore necessary. Often a Gaussian shaped point spread function 
IAPRS, Vol. 30, Part 5W1, ISPRS Intercommission Workshop "From Pixels to Sequences", Zurich, March 22-24 1995