Bayesian recognition of local 3-d shape by approximating image intensity functions with quadric polynomials

The recognition in image data of viewed patches of spheres, cylinders, and planes in the 3-D world is discussed as a first step to complex object recognition or complex object location and orientation estimation. Accordingly, an image is partitioned into small square windows, each of which is a view of a piece of a sphere, or of a cylinder, or of a plane. Windows are processed in parallel for recognition of content. New concepts and techniques include approximations of the image within a window by 2-D quadric polynomials where each approximation is constrained by one of the hypotheses that the 3-D surface shape seen is either planar, cylindrical, or spherical; a recognizer based upon these approximations to determine whether the object patch viewed is a piece of a sphere, or a piece of a cylinder, or a piece of a plane; lowpass filtering of the image by the approximation. The shape recognition is computationally simple, and for large windows is approximately Bayesian minimum-probability-of-error recognition. These classifications are useful for many purposes. One such purpose is to enable a following processor to use an appropriate estimator to estimate shape, and orientation and location parameters for the 3-D surface seen within a window.     

Fast computation of the difference of low-pass transform

This paper defines the difference of low-pass (DOLP) transform and describes a fast algorithm for its computation. The DOLP is a reversible transform which converts an image into a set of bandpass images. A DOLP transform is shown to require O(N2) multiplies and produce O(N log(N)) samples from an N sample image. When Gaussian low-pass filters are used, the result is a set of images which have been convolved with difference of Gaussian (DOG) filters from an exponential set of sizes. A fast computation technique based on ``resampling' is described and shown to reduce the DOLP transform complexity to O(N log(N)) multiplies and O(N) storage locations. A second technique, ``cascaded convolution with expansion,' is then defined and also shown to reduce the computational cost to O(N log(N)) multiplies. Combining these two techniques yields an algorithm for a DOLP transform that requires O(N) storage cells and requires O(N) multiplies.     

Odour emission ability (OEA) and its application in assessing odour removal efficiency

Odourous emissions from sewer networks and wastewater treatment plants (WWTPs) can significantly impact a local population. Sampling techniques such as wind tunnels and flux hood chambers are traditionally used to collect area source samples for subsequent quantification of odour emission rates using dilution olfactometry, however these methods are unsuitable for assessing liquid samples from point sources due to the large liquid volumes required. To overcome this limitation, a gas phase sample preparation method was developed for assessing the total Odour Emission Ability (OEA) from a liquid sample. The method was validated using two volatile organic sulphur compounds (VOSCs), dimethyl-trisulphide (DMTS) and bismethylthiomethane (BMTM) that are frequently detected from sewers and WWTPs and are relatively stable compared with common VOSCs like mercaptan or methyl mercaptan. The recovery rates of DMTS and BMTM were quantified by injecting a known volume of a standard liquid sample into Tedlar bags using a static injection and a dynamic injection methodology. It was confirmed that both dynamic and static injection methods at ambient condition achieved high recovery rates with no need to consider increasing evaporation by elevating the temperature. This method can also be used to assess odour removal effectiveness of liquids by comparing the OEA before and after the treatment tests. Two application examples were presented.     

Reconstruction from Sparsely Sampled Data by ART with Interpolated Rays

After a brief discussion of the algebraic reconstruction techniques (ART), we introduce the attenuation problem in positron emission tomography (PET). We anticipate that a generalization of ART, the so-called cyclic subgradient projection (CSP) method, may be useful for solving this problem. This, however, has not been successfully realized, due to the fact that data collected by our proposed stationary PET detector ring are too sparsely sampled. That this is, in fact, a major problem is demonstrated by showing that ordinary ART produces reconstructions with unacceptably strong artifacts even on perfect (no attenuation) data collected according to the PET geometry. We demonstrate that the source of this artifact is the sparse sampling, and we propose the use of interpolated rays to overcome the problem. This approach is successful, as is illustrated by showing reconstructions from sparsely sampled data by ART with interpolated rays.