Clusters of fine, granular microcalcifications in mammograms may be an early sign of disease. Individual grains are difficult to detect and segment due to size and shape variability and because the background mammogram texture is typically inhomogeneous. The authors develop a 2-stage method based on wavelet transforms for detecting and segmenting calcifications. The first stage is based on an undecimated wavelet transform, which is simply the conventional filter bank implementation without downsampling, so that the low-low (LL), low-high (LH), high-low (HL), and high-high (HH) sub-bands remain at full size. Detection takes place in HH and the combination LH+HL. Four octaves are computed with 2 inter-octave voices for finer scale resolution. By appropriate selection of the wavelet basis the detection of microcalcifications in the relevant size range can be nearly optimized. In fact, the filters which transform the input image into HH and LH+HL are closely related to prewhitening matched filters for detecting Gaussian objects (idealized microcalcifications) in 2 common forms of Markov (background) noise. The second stage is designed to overcome the limitations of the simplistic Gaussian assumption and provides an accurate segmentation of calcification boundaries. Detected pixel sites in HH and LH+HL are dilated then weighted before computing the inverse wavelet transform. Individual microcalcifications are greatly enhanced in the output image, to the point where straightforward thresholding can be applied to segment them. FROG curves are computed from tests using a freely distributed database of digitized mammograms.

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We show that a biorthogonal spline wavelet closely approximates the prewhitening matched filter for detecting Gaussian objects in Markov noise. The filterbank implementation of the wavelet transform acts as a hierarchy of such detectors operating at discrete object scales. If the object to be detected is Gaussian and its scale happens to coincide with one of those computed by the wavelet transform, and if the background noise is truly Markov, then optimum detection is realized by thresholding the appropriate subband image. In reality, the Gaussian may be a rather coarse approximation of the object, and the background noise may deviate from the Markov assumption. In this case, we may view the wavelet decomposition as a means for computing an orthogonal feature set for input to a classifier. We use a supervised linear classifier applied to feature vectors comprised of samples taken from the subbands of an N-octave, undecimated wavelet transform. The resulting map of test statistic values indicates the presence and location of objects. The object itself is reconstructed by using the test statistic to emphasize wavelet subbands, followed by computing the inverse wavelet transform. We show two contrasting applications of the wavelets-based object recovery algorithm. For detecting microcalcifications in digitized mammograms, the object and noise models closely match the real image data, and the multiscale matched filter paradigm is highly appropriate. The second application, extracting ship outlines in noisy forward-looking infrared images, is presented as a case where good results are achieved despite the data models being less well matched to the assumptions of the algorithm.

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An imaging photopolarimeter aboard Pioneer 11, including a 2.5-centimeter telescope, was used for 2 weeks continuously in August and September 1979 for imaging, photometry, and polarimetry observations of Saturn, its rings, and Titan. A new ring of optical depth < 2 x 10(-3) was discovered at 2.33 Saturn radii and is provisionally named the F ring; it is separated from the A ring by the provisionally named Pioneer division. A division between the B and C rings, a gap near the center of the Cassini division, and detail in the A, B, and C rings have been seen; the nomenclature of divisions and gaps is redefined. The width of the Encke gap is 876 +/- 35 kilometers. The intensity profile and colors are given for the light transmitted by the rings. A mean particle size less, similar 15 meters is indicated; this estimate is model-dependent. The D ring was not seen in any viewing geometry and its existence is doubtful. A satellite, 1979 S 1, was found at 2.53 +/- 0.01 Saturn radii; the same object was observed approximately 16 hours later by other experiments on Pioneer 11. The equatorial radius of Saturn is 60,000 +/- 500 kilometers, and the ratio of the polar to the equatorial radius is 0.912 +/- 0.006. A sample of polarimetric data is compared with models of the vertical structure of Saturn's atmosphere. The variation of the polarization from the center of the disk to the limb in blue light at 88 degrees phase indicates that the density of cloud particles decreases as a function of altitude with a scale height about one-fourth that of the gas. The pressure level at which an optical depth of 1 is reached in the clouds depends on the single-scattering polarizing properties of the clouds; a value similar to that found for the Jovian clouds yields an optical depth of 1 at about 750 millibars.