Restoration of subtractive noise on a binary image by a single morphological operation, closing, is analyzed. Restoration by closing alone is appropriate under particular explicitly defined random noise models, based respectively on erosion, independent pixel subtractive noise, and independent pixel subtractive noise followed by dilation. Since in general it is not possible to perfectly restore subtractive noise, we use the Hausdorff metric to measure the residual error in restoration. This metric is an appropriate one because of its geometric interpretation in terms of set coverings. We describe a best first search procedure to find a structuring element for closing that is optimal in the sense of minimizing the mean Hausdorff error. The search procedure's utility function is based on the calculation of certain probabilities related to the noise model, namely the probability of one set being the subset of another set and some related probabilities. We describe how a bound on these probabilities can be efficiently computed to speed up the search process.

A fully automatic algorithm was developed for single-frame detection of minelike objects in realistic shallow water, beach, and nearby land environments. Detection was accomplished in gray scale images, containing representative targets and backgrounds, which had been collected by a down-looking coherent active sensor. The problem was made challenging by low contrast, partly covered targets, and highly cluttered images including beach vegetation and rocks, complicated natural backgrounds, obscuration (replacement noise) by glint from the surface of the water and distortion within it, and 15 kinds of manmade objects. To deal with these challenges, innovations have been made in automatic background cancellation, in the final thresholding to binary, and in shape and veracity clues for the feature vector used in the final classification step. Performance is reported for a representative set of 1024 frames. For the majority of background types, including low conventional signal-to-noise ratio and pervasive instances of clutter and replacement noise patches, the algorithm performed correctly in 92% of the frames. This applies individually to frames identified as 'target' where one or more targets existed, and frames identified as 'notarget' where no targets existed. Target-field detection over multiple frames depends upon reliable single-frame target detection. Despite challenging images, performance of our single-frame algorithm appears sufficient for multiframe target-field detection to proceed with acceptable error rates for the majority of background types encountered in the tests conducted.

Split-beam sonar binary images are inherently noisy and have large quantities of shot noise as well as many missing data points. We address the problem of their restoration via mathematical morphology. Conventional restoration techniques for these types of images do not make use of any of the spatial relationships between data points, such as a qualitative observation that outliers tend to have much larger distances to neighboring pixels. We first define an explicit noise model that characterizes the image degradation process for split-beam sonar images. A key feature of the model is that the degradation is split into two parts, a foreground component and a background component. The amount of noise occurring in the background decreases with distance from the underlying signal object. Thus outliers in the model have the same statistical properties as those observed in training data. Next we propose two different restoration algorithms for these kinds of images based respectively on morphological distance transforms and dilation with a toroid shaped structuring element followed by intersection. Finally we generalize to processing other kinds of imagery where applicable.

This paper analyzes restoration of subtractive noise on a binary image by a single morphological operation, dilation. Restoration by dilation alone is appropriate under particular explicitly defined random noise models, based respectively on erosion, independent pixel subtractive noise, and independent pixel subtractive noise followed by dilation. Since in general it is not possible to perfectly restore subtractive noise we use the Hausdorf metric to measure the residual error in restoration. This metric is the appropriate one because of its geometric interpretation in terms of set coverings. We describe a search procedure to find a structuring element for dilation that is optimal in the sense of minimizing the mean Hausdorf error. The search procedure's utility function is based on the calculation of certain probabilities related to the noise model, namely the probability of one set being the subset of another set and some related probabilities.

This paper presents a case study of the design of a fully autonomous morphological detection algorithm. Grayscale input images contain objects to be detected among difficult clutter, replacement noise, and background tilt. The criteria for choosing algorithm structure is included, with associated grayscale and binary structuring elements based upon comparing the geometry of target and noise/clutter objects. Background cancellation is discussed, along with histogram-based techniques for final thresholding to binary detection images. Finally a performance characterization methodology for the detection algorithm is presented. In addition to conventional detection statistics, the authors consider the 'quality' of the hits and false alarms, vis-a-vis the feature set and classifier used in classification downstream of the detector in the overall system design.