Channelized detection filters.

The problem of detecting objects in noisy backgrounds is addressed. We derive detection filters by training a linear classifier, using features obtained from subimages corresponding to circular channels in the Fourier domain. The classifier weights approach the prewhitening matched filter when the classifier is trained for the detection of known objects in stationary noise. A simple form of rotation invariance is attained for considerably less computation than by the direct application of multiple matched filters. The method is demonstrated for the task of detecting simulated tumors in simulated nuclear medical images.

Wavelet transform methods for object detection and recovery.

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.

Wavelet transforms for detecting microcalcifications in mammograms.

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.

Tumor detection in nonstationary backgrounds.

The authors introduce two detectors which they use to locate simulated tumors of fixed size in clinical gamma-ray images. The first method was conceived when it was observed that small tumors possess an identifiable signature in curvature feature space, where "curvature" is the local curvature of the image data when viewed as a relief map. Computed curvature values are mapped to a normalized significance space using a windowed statistic. The resulting test statistic is thresholded at a chosen level of significance to give a positive detection. Nonuniform anatomic background activity is effectively suppressed. The second detector is an adaptive prewhitening matched filter, which uses a form of preprocessing known as statistical scaling to adaptively prewhiten the background. Tests are performed using simulated Gaussian-shaped tumors superimposed on twelve clinical gamma ray images. When the tumors to be detected are small-less than 3 pixels in diameter-the curvature detector out-performs the matched filter in true positive/false positive tests. A mean true positive rate of 95% at one false positive per image is achieved when the local signal-to-noise ratio of the tumor-background is >/=2. At larger tumor sizes the best performance is displayed by a different form of matched filter, namely the statistical correlation function proposed by Pratt (1991).

Reconstruction of an axisymmetric image from its blurred and noisy projection.

The 3-D velocity distribution of ionized photofragments resulting from the dissociation of methyl iodide is recovered by digitally deblurring and Abel inverting a single measured 2-D projection. The reconstructed distribution reveals two rings which are the dissociation channels corresponding to ground state and excited state iodine. A factor of 1.6 in resolution improvement of the channels is achieved by deconvolving the 2-D projection using a line-by-line implementation of Kawata's reblur algorithm. This technique guarantees noise-smoothed projections for the notoriously sensitive Abel inversion procedure, which in this paper is implemented using discrete Fourier and Hankel transforms.

Optical flow computation in combustion image sequences.

A time-resolved sequence of laser shadowgraph images is computer processed to produce 2-D optical flow maps showing the motion of the combustion interface between hot products and cold reactants. Background-subtracted shadowgraph images are reduced to skeletons, followed by local correlation between adjacent frames for computing optical flow. The resulting flow maps represent an initial step toward the goal of computer-assisted flowfield analysis and interpretation.

Rectification and enhancement of three severely distorted images of Jupiter's north polar region.

A number of high-resolution images of Jupiter's northern hemisphere were received from the imaging photo-polarimeter (IPP) aboard Pioneer 11 in 1974. Erratic scanning of the IPP caused severe distortions in three scientifically important images, which until now have never been satisfactorily restored. We report new rectification and enhancement techniques, implemented on up-to-date image processing hardware, yielding images of sufficient quality to enable full scientific exploitation of the photometric data.

Imaging photopolarimeter on pioneer saturn.

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.