We present a method for deriving a parametric description of a conic section (quadratic curve) in an image from the moments of the image with respect to several specially-constructed kernel functions. In contrast to Hough-transform-type methods, the moment approach requires no large accumulator array. Judicious implementation allows the parameters to be determined using five multiplication operations and six addition operations per pixel. The use of moments renders the calculation robust in the presence of high-frequency noise or texture and resistant to small-scale irregularities in the edge. Our method is generalizable to more complex classes of curves with more parameters as well as to surfaces in higher dimensions.

In a grayscale image to be binarized, some pixels represent "foreground" text, to be converted to black-while others represent a shaded "background" region, to be converted to white. The difference between the two is largely one of scale. Morphological operators, the alternating sequential filter in particular, though an effective tool for extracting image background, are computationally expensive. We define reduced-complexity quick-open and quick-close morphological operators, which are employed to binarize grayscale images having complex backgrounds at modest computational cost.

We present a method of locating edges in JPEG-coded images which operates in frequency space on the DCT coefficients. Applied to the quantized DCT coefficients of a block containing a straight edge, the method yields an equation for the edge in a fraction of the operations needed to dequantize and transform the coefficents to pixel values. As a sample application of this method, we present a technique for alleviating ringing artifacts in JPEG-coded images.

The method of custom-built moments allows location of step edges in an image in parametric form, as an equation ax+by=c, using a customizable mask of almost any desired shape, or moment functions adapted to calculation in a particular basis. We adapt this method to the problem of locating both thin lines and roof edges in parametric form.

We present a general construction of functions whose moments serve to locate and parametrize step edges within an image. Previous use of moments to locate edges was limited to functions supported on a circular region, but our method allows the use of "custom-designed" functions supported on circles, rectangles, or any desired shape, and with graphs whose shape may be chosen with great freedom. We present analyses of the sensitivity of our method to pixelization errors or discrepancy between the image and an idealized edge model. The parametric edge description yielded by our method makes it especially suitable as a component of wedgelet image coding.

We introduce the eidochromatic transform as a tool for improved lossy coding of color images. Many current image-coding formats (such as JPEG 2000) utilize both a color-component transform (relating values of different image components at a single location) and a wavelet or other spatial transform (relating values of a single-image component at proximate, but different image locations). The eidochromatic transform further reduces redundancy by relating image values simultaneously across color components and in the two spatial dimensions. Our approach is to introduce an additional transform step following the color-component and spatial transforms. In tests, this step reduced the overall static entropy of the chrominance components of quantized transformed images by up to 40% or more. Combined with JPEG 2000's modeling and coding method, the eidochromatic transform was found to reduce the size of lossily coded color images by up to 27% overall.

We present a new integrated algorithm for binary arithmetic coding and probability estimation, competitive in speed and compression performance with state-of-the-art algorithms such as the QM-coder and Z-coder. The chief innovation is representing the bracketing interval width both directly and by a logarithmic approximation. Performance is evaluated by experiments using bilevel-image data sets. An open-source software version is available.