A fast and flexible algorithm for computing watersheds in digital gray-scale images is introduced. A review of watersheds and related motion is first presented, and the major methods to determine watersheds are discussed. The algorithm is based on an immersion process analogy, in which the flooding of the water in the picture is efficiently simulated using of queue of pixel. It is described in detail provided in a pseudo C language. The accuracy of this algorithm is proven to be superior to that of the existing implementations, and it is shown that its adaptation to any kind of digital grid and its generalization to n-dimensional images (and even to graphs) are straightforward. The algorithm is reported to be faster than any other watershed algorithm. Applications of this algorithm with regard to picture segmentation are presented for magnetic resonance (MR) imagery and for digital elevation models. An example of 3-D watershed is also provided. >

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Watersheds in digital spaces: an efficient algorithm based on immersion simulations

The Hausdorff distance measures the extent to which each point of a model set lies near some point of an image set and vice versa. Thus, this distance can be used to determine the degree of resemblance between two objects that are superimposed on one another. Efficient algorithms for computing the Hausdorff distance between all possible relative positions of a binary image and a model are presented. The focus is primarily on the case in which the model is only allowed to translate with respect to the image. The techniques are extended to rigid motion. The Hausdorff distance computation differs from many other shape comparison methods in that no correspondence between the model and the image is derived. The method is quite tolerant of small position errors such as those that occur with edge detectors and other feature extraction methods. It is shown that the method extends naturally to the problem of comparing a portion of a model against an image. >

Comparing images using the Hausdorff distance

Humans perceive the three-dimensional structure of the world with apparent ease. However, despite all of the recent advances in computer vision research, the dream of having a computer interpret an image at the same level as a two-year old remains elusive. Why is computer vision such a challenging problem and what is the current state of the art? Computer Vision: Algorithms and Applications explores the variety of techniques commonly used to analyze and interpret images. It also describes challenging real-world applications where vision is being successfully used, both for specialized applications such as medical imaging, and for fun, consumer-level tasks such as image editing and stitching, which students can apply to their own personal photos and videos. More than just a source of recipes, this exceptionally authoritative and comprehensive textbook/reference also takes a scientific approach to basic vision problems, formulating physical models of the imaging process before inverting them to produce descriptions of a scene. These problems are also analyzed using statistical models and solved using rigorous engineering techniques Topics and features: structured to support active curricula and project-oriented courses, with tips in the Introduction for using the book in a variety of customized courses; presents exercises at the end of each chapter with a heavy emphasis on testing algorithms and containing numerous suggestions for small mid-term projects; provides additional material and more detailed mathematical topics in the Appendices, which cover linear algebra, numerical techniques, and Bayesian estimation theory; suggests additional reading at the end of each chapter, including the latest research in each sub-field, in addition to a full Bibliography at the end of the book; supplies supplementary course material for students at the associated website, http://szeliski.org/Book/. Suitable for an upper-level undergraduate or graduate-level course in computer science or engineering, this textbook focuses on basic techniques that work under real-world conditions and encourages students to push their creative boundaries. Its design and exposition also make it eminently suitable as a unique reference to the fundamental techniques and current research literature in computer vision.

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Computer Vision: Algorithms and Applications

Foundations of Confocal Scanned Imaging in Light Microscopy -- Fundamental Limits in Confocal Microscopy -- Special Optical Elements -- Points, Pixels, and Gray Levels: Digitizing Image Data -- Laser Sources for Confocal Microscopy -- Non-Laser Light Sources for Three-Dimensional Microscopy -- Objective Lenses for Confocal Microscopy -- The Contrast Formation in Optical Microscopy -- The Intermediate Optical System of Laser-Scanning Confocal Microscopes -- Disk-Scanning Confocal Microscopy -- Measuring the Real Point Spread Function of High Numerical Aperture Microscope Objective Lenses -- Photon Detectors for Confocal Microscopy -- Structured Illumination Methods -- Visualization Systems for Multi-Dimensional Microscopy Images -- Automated Three-Dimensional Image Analysis Methods for Confocal Microscopy -- Fluorophores for Confocal Microscopy: Photophysics and Photochemistry -- Practical Considerations in the Selection and Application of Fluorescent Probes -- Guiding Principles of Specimen Preservation for Confocal Fluorescence Microscopy -- Confocal Microscopy of Living Cells -- Aberrations in Confocal and Multi-Photon Fluorescence Microscopy Induced by Refractive Index Mismatch -- Interaction of Light with Botanical Specimens -- Signal-to-Noise Ratio in Confocal Microscopes -- Comparison of Widefield/Deconvolution and Confocal Microscopy for Three-Dimensional Imaging -- Blind Deconvolution -- Image Enhancement by Deconvolution -- Fiber-Optics in Scanning Optical Microscopy -- Fluorescence Lifetime Imaging in Scanning Microscopy -- Multi-Photon Molecular Excitation in Laser-Scanning Microscopy -- Multifocal Multi-Photon Microscopy -- 4Pi Microscopy -- Nanoscale Resolution with Focused Light: Stimulated Emission Depletion and Other Reversible Saturable Optical Fluorescence Transitions Microscopy Concepts -- Mass Storage, Display, and Hard Copy -- Coherent Anti-Stokes Raman Scattering Microscopy -- Related Methods for Three-Dimensional Imaging -- Tutorial on Practical Confocal Microscopy and Use of the Confocal Test Specimen -- Practical Confocal Microscopy -- Selective Plane Illumination Microscopy -- Cell Damage During Multi-Photon Microscopy -- Photobleaching -- Nonlinear (Harmonic Generation) Optical Microscopy -- Imaging Brain Slices -- Fluorescent Ion Measurement -- Confocal and Multi-Photon Imaging of Living Embryos -- Imaging Plant Cells -- Practical Fluorescence Resonance Energy Transfer or Molecular Nanobioscopy of Living Cells -- Automated Confocal Imaging and High-Content Screening for Cytomics -- Automated Interpretation of Subcellular Location Patterns from Three-Dimensional Confocal Microscopy -- Display and Presentation Software -- When Light Microscope Resolution Is Not Enough:Correlational Light Microscopy and Electron Microscopy -- Databases for Two- and Three-Dimensional Microscopical Images in Biology -- Confocal Microscopy of Biofilms — Spatiotemporal Approaches -- Bibliography of Confocal Microscopy.

Handbook of biological confocal microscopy

Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science (2nd edition)

Euclidean distance mapping

In a scanning laser microscope detecting fluorescent light from the specimen, the depth-discriminating property of confocal scanning has been used to carry out optical slicing of a thick specimen. The recorded digital images constitute a three-dimensional raster covering a volume of the specimen. The specimen has been visualized in stereo and rotation by making look-through projections of the digital data in different directions. The contrast of the pictures has been enhanced by generating the gradient volume. This permits display of the border surfaces between regions instead of the regions themselves.

Three-dimensional microscopy using a confocal laser scanning microscope.

Generalized and Separable Sobel Operators

Contemporary reconstruction methods employed for clinical helical cone-beam computed tomography (CT) are analytical (noniterative) but mathematically nonexact, i.e., the reconstructed image contains so called cone-beam artifacts, especially for higher cone angles. Besides cone artifacts, these methods also suffer from windmill artifacts: alternating dark and bright regions creating spiral-like patterns occurring in the vicinity of high z-direction derivatives. In this article, the authors examine the possibility to suppress cone and windmill artifacts by means of iterative application of nonexact three-dimensional filtered backprojection, where the analytical part of the reconstruction brings about accelerated convergence. Specifically, they base their investigations on the weighted filtered backprojection method [Stierstorfer et al., Phys. Med. Biol. 49, 2209-2218 (2004)]. Enhancement of high frequencies and amplification of noise is a common but unwanted side effect in many acceleration attempts. They have employed linear regularization to avoid these effects and to improve the convergence properties of the iterative scheme. Artifacts and noise, as well as spatial resolution in terms of modulation transfer functions and slice sensitivity profiles have been measured. The results show that for cone angles up to +/-2.78 degrees, cone artifacts are suppressed and windmill artifacts are alleviated within three iterations. Furthermore, regularization parameters controlling spatial resolution can be tuned so that image quality in terms of spatial resolution and noise is preserved. Simulations with higher number of iterations and long objects (exceeding the measured region) verify that the size of the reconstructible region is not reduced, and that the regularization greatly improves the convergence properties of the iterative scheme. Taking these results into account, and the possibilities to extend the proposed method with more accurate modeling of the acquisition process, the authors believe that iterative improvement with non-exact methods is a promising technique for medical CT applications.

Per-Erik Danielsson

Papers

Euclidean distance mapping

Three-dimensional microscopy using a confocal laser scanning microscope.

Generalized and Separable Sobel Operators

Regularized iterative weighted filtered backprojection for helical cone-beam CT

High-accuracy rotation of images