Nevoscopy: three-dimensional computed tomography of nevi and melanomas in situ by transillumination

The thickness of a malignant nevus has been found to be an important prognostic factor for patients with melanoma. We have designed a new method of imaging nevi that permits their thickness to be measured in situ. Using fiber optics directed into the surrounding skin, we transilluminate the nevus. Three images are picked up by a digitizing TV camera: the vertical image (90 degrees ), a glancing image (180 degrees ), and one at 45 degrees , obtained by using two front-silvered mirrors held next to the nevus in a "nevoscope." The digitized images are used in a computed tomography algorithm to calculate approximate vertical cross sections of the nevus. The algorithm is one we recently developed to permit reconstruction from a very few projections. Our method is completely noninvasive. It may be used to check all the nevi on a patient. Without excisions, we could establish a baseline three-dimensional shape for each nevus, follow any changes in time, and obtain an early warning of increase in thickness and possible malignancy.     

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.