Preface 1. The approximation problem and existence of best approximations 2. The uniqueness of best approximations 3. Approximation operators and some approximating functions 4. Polynomial interpolation 5. Divided differences 6. The uniform convergence of polynomial approximations 7. The theory of minimax approximation 8. The exchange algorithm 9. The convergence of the exchange algorithm 10. Rational approximation by the exchange algorithm 11. Least squares approximation 12. Properties of orthogonal polynomials 13. Approximation of periodic functions 14. The theory of best L1 approximation 15. An example of L1 approximation and the discrete case 16. The order of convergence of polynomial approximations 17. The uniform boundedness theorem 18. Interpolation by piecewise polynomials 19. B-splines 20. Convergence properties of spline approximations 21. Knot positions and the calculation of spline approximations 22. The Peano kernel theorem 23. Natural and perfect splines 24. Optimal interpolation Appendices Index.

Approximation theory and methods, by M. J. D. Powell. Pp 339. £25 (hardcover), £8·50 (paperback). 1981. ISBN 0-521-22472-1/29514-9 (Cambridge University Press)

The watershed transform has interesting properties that make it useful for many different image segmentation applications: it is simple and intuitive, can be parallelized, and always produces a complete division of the image. However, when applied to medical image analysis, it has important drawbacks (oversegmentation, sensitivity to noise, poor detection of thin or low signal to noise ratio structures). We present an improvement to the watershed transform that enables the introduction of prior information in its calculation. We propose to introduce this information via the use of a previous probability calculation. Furthermore, we introduce a method to combine the watershed transform and atlas registration, through the use of markers. We have applied our new algorithm to two challenging applications: knee cartilage and gray matter/white matter segmentation in MR images. Numerical validation of the results is provided, demonstrating the strength of the algorithm for medical image segmentation.

Improved watershed transform for medical image segmentation using prior information

Given a large dataset of images, we seek to automatically determine the visually similar object and scene classes together with their image segmentation. To achieve this we combine two ideas: (i) that a set of segmented objects can be partitioned into visual object classes using topic discovery models from statistical text analysis; and (ii) that visual object classes can be used to assess the accuracy of a segmentation. To tie these ideas together we compute multiple segmentations of each image and then: (i) learn the object classes; and (ii) choose the correct segmentations. We demonstrate that such an algorithm succeeds in automatically discovering many familiar objects in a variety of image datasets, including those from Caltech, MSRC and LabelMe.

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Using Multiple Segmentations to Discover Objects and their Extent in Image Collections

This paper presents a computational paradigm called Data-Driven Markov Chain Monte Carlo (DDMCMC) for image segmentation in the Bayesian statistical framework. The paper contributes to image segmentation in four aspects. First, it designs efficient and well-balanced Markov Chain dynamics to explore the complex solution space and, thus, achieves a nearly global optimal solution independent of initial segmentations. Second, it presents a mathematical principle and a K-adventurers algorithm for computing multiple distinct solutions from the Markov chain sequence and, thus, it incorporates intrinsic ambiguities in image segmentation. Third, it utilizes data-driven (bottom-up) techniques, such as clustering and edge detection, to compute importance proposal probabilities, which drive the Markov chain dynamics and achieve tremendous speedup in comparison to the traditional jump-diffusion methods. Fourth, the DDMCMC paradigm provides a unifying framework in which the role of many existing segmentation algorithms, such as, edge detection, clustering, region growing, split-merge, snake/balloon, and region competition, are revealed as either realizing Markov chain dynamics or computing importance proposal probabilities. Thus, the DDMCMC paradigm combines and generalizes these segmentation methods in a principled way. The DDMCMC paradigm adopts seven parametric and nonparametric image models for intensity and color at various regions. We test the DDMCMC paradigm extensively on both color and gray-level images and some results are reported in this paper.

Image segmentation by data-driven Markov chain Monte Carlo

An enhanced text entry system using word-level analysis to automatically correct inaccuracies in user keystroke entries on reduced keyboards. The keyboard (105) may be a part of a touch-sensitive panel or display screen (100) or on a mechanical keyboard system. A method and system are defined which determine one or more alternative textual interpretations of each sequence of inputs detected within a designated auto-correcting keyboard region (106). The actual contact locations for the keystrokes may occur outside the boundaries of the specific keyboard key regions, where the distance from each contact location to each corresponding intended character may in general increase with the expected frequency of the intended word in the language or in a particular context. The user can easily select the intended word from among the generated interpretations.

Keyboard system with automatic correction

In this work, a new approach to fully automatic color image segmentation, called JSEG, is presented. First, colors in the image are quantized to several representing classes that can be used to differentiate regions in the image. Then, image pixel colors are replaced by their corresponding color class labels, thus forming a class-map of the image. A criterion for "good" segmentation using this class-map is proposed. Applying the criterion to local windows in the class-map results in the "J-image", in which high and low values correspond to possible region boundaries and region centers, respectively. A region growing method is then used to segment the image based on the multi-scale J-images. Experiments show that JSEG provides good segmentation results on a variety of images.

Color image segmentation

A color image processing method for retrieving a color feature descriptor for describing color features of an image is provided. The color image processing method includes the steps of (a) obtaining color vectors of an input image, (b) classifying the color vectors to obtain dominant colors of the input image and the ratios thereof, and (c) representing the dominant colors and the ratios thereof as a color feature descriptor of the input image. The color image processing method is applied to an object-based image processing method, thereby allowing fast search and retrieval of multi-media contents.

Color image processing method and apparatus thereof

A database building method for multimedia contents is provided. The database building method for multimedia contents has the steps of (a) accessing an arbitrary site providing multimedia contents through a telecommunications network; (b) calling multimedia contents in by spidering the site; and (c) classifying the multimedia contents data according to the stored addresses and storing them in a predetermined database. Using category information on the corresponding sites, the database building method for multimedia contents according to the present invention semantically classifies multimedia contents and stores them in the corresponding databases. In the database built by the database building method for multimedia contents according to the present invention, multimedia contents which are dispersed on the WWW are well collected and, using category information or URL information, are semantically well classified. Therefore, various method for retrieving multimedia contents can be used so that wanted multimedia contents can be retrieved fast and efficiently.

Database building method for multimedia contents

A method describes activity in a video sequence. The method measures intensity, direction, spatial, and temporal attributes in the video sequence, and the measured attributes are combined in a digital descriptor of the activity of the video sequence.

Activity descriptor for video sequences

An apparatus for searching a digital image and a method therefor are provided. The digital image search apparatus includes a database processing unit for segmenting an image from the database or an image which is not stored in the database into homogeneous regions and analyzing and storing the segmented regions and an image search engine unit for searching for an image having a segmented region showing a characteristic similar to the characteristic of the query region. It is possible to perform detailed and efficient searching work since it is possible to perform a region-based search by means of segmented regions and a user can perform searching by selecting the characteristic and the position of the segmented regions.

Hyun-Doo Shin

Papers

Color image segmentation

Color image processing method and apparatus thereof

Database building method for multimedia contents

Activity descriptor for video sequences

Method and apparatus for searching a digital image