Wavelet Compression of Three-Dimensional Time-Lapse Biological Image Data H. Narfi Stefansson, 1 Kevin W. Eliceiri, 2, * Charles F. Thomas, 2 Amos Ron, 1 Ron DeVore, 3 Robert Sharpley, 3 and John G. White 2 1 Department of Mathematics and Computer Science, University of Wisconsin, Madison, WI 53706, USA 2 Laboratory for Optical and Computational Instrumentation, University of Wisconsin, Madison, WI 53706, USA 3 Department of Mathematics, University of South Carolina, Columbia, SC 29208, USA Abstract: The use of multifocal-plane, time-lapse recordings of living specimens has allowed investigators to visualize dynamic events both within ensembles of cells and individual cells. Recordings of such four- dimensional ~4D! data from digital optical sectioning microscopy produce very large data sets. We describe a wavelet-based data compression algorithm that capitalizes on the inherent redunancies within multidimen- sional data to achieve higher compression levels than can be obtained from single images. The algorithm will permit remote users to roam through large 4D data sets using communication channels of modest bandwidth at high speed. This will allow animation to be used as a powerful aid to visualizing dynamic changes in three-dimensional structures. Key words: wavelet image data compression, digital microscopy I NTRODUCTION Much of our knowledge of the biological world has been obtained through the study of images. Research scientists use images from microscopes to understand the workings of a cell, the development of an organism, or the pathological state of a tissue. The use of microscopy to study living specimens has gained considerable momentum recently. This is primarily the result of the combined use of genome sequence data and fluorescent protein reporter technology, which has allowed the distribution of any protein to be observed in cells, tissues, or even embryos ~Chalfie et al., 1994!. Developments in microscopy have allowed optical sections to be visualized within intact tissue, thereby obviat- ing the need for the microscopists’ traditional strategy of cutting sections in order to reconstruct three-dimensional ~3D! data. Techniques for optical sectioning have been developed that can provide 3D data from living specimens. Nomarski imaging is a relatively simple technique that uses gradients of refractive index to produce contrast ~Nomarski, 1955!. It is the most benign of the optical sectioning techniques but has little specificity. On the other hand, fluorescence micros- copy used in conjunction with fluorescent protein reporters can be used to reveal the distribution of a selected few molecular species out of the 100,000 components that typi- cally make up a living organism. However, this technique can give rise to problems of phototoxicity. The newly devel- oped optical sectioning technique of multiphoton fluores- cence excitation ~MPFE! imaging produces low levels of photoxicity and can obtain images considerably deeper into a specimen than the other commonly used fluorescence optical sectioning method, confocal imaging ~Denk et al., 1990; Centonze & White, 1998!. Using MPFE imaging, we have shown that it is possible to make continuous multifocal- plane, time-lapse recordings of a vertebrate embryo for 24 h without compromising viability or developmental potency ~Squirrell et al., 1999!. To visualize dynamic processes in three dimensions using optical sectioning microscopy, multifocal-plane, time- lapse movies are often used. These movies are recorded digitally by a computer that is interfaced to the microscope. The computer controls microscope focus and image cap- ture. Using multidimensional image viewing applications ~Thomas et al., 1996; Eliceiri et al., 2002! an investigator can roam through four-dimensional ~4D; 3D plus time! data sets in space and time using animation as an aid to visualiz- ing dynamic processes occurring within the recording. This technique is proving to be a very powerful way of visualiz- ing both developmental processes involving sheets of cells moving in three dimensions and intercellular processes involving dynamic changes to cytoarchitecture such as those that occur during cell division. In the course of our studies on the early development of the nematode, Caenorhabditis elegans, we have assembled large numbers of 4D recordings depicting the early develop- Received October 28, 2003; accepted January 15, 2004. *Corresponding author. E-mail: eliceiri@wisc.edu Microsc. Microanal. 11, 9–17, 2005 DOI: 10.1017/S1431927605050014 Microscopy AND Microanalysis © MICROSCOPY SOCIETY OF AMERICA 2005