Transformation of adaptive thresholds by significance invariance for change detection

Abstract

The detection of changes in image sequences often is the first essential step to video analysis, e.g. for the detection, classification and tracking of moving objects. As a binary classification problem, change detection is afflicted by the trade-off between two class error probabilities, viz. the rates of false positives and false negatives. In this contribution, we derive an adaptive two-threshold scheme to improve on this trade-off. The threshold selection for each pixel in the current frame is controlled by the previous detection result for this pixel. Since the test statistics are calculated from samples comprising several pixels within a local sliding window, a transformation of the thresholds from the singlepixel observations to decisions based on larger samples is required. Based on the fact that we can only model the null hypothesis, i.e., absence of motion, realistically, we suggest to transform the threshold under the constraint of a constant false-positive rate, or significance invariance. The resulting detection algorithm is only marginally more complex than a straightforward global thresholding procedure, while providing visibly improved results.

Segmentation of retinal vessels with a hysteresis binary-classification paradigm

“…When segmenting by thresholding, in a majority of cases a single fixed, global threshold [30] is used for all pixels. There are also adaptive approaches where several thresholds are employed [24], [31], and, in the limit, each pixel obtains its own threshold [32]. The hysteresis paradigm in this case yields an adaptive approach [25] with two thresholds, each corresponding to a base classifier.…”

Multiscale NeighborhoodWise Decision Fusion for Redundancy Detection in Image Pairs

“…There has been a substantial amount of work to handle changes in an image pair [3,99,2,86,66,80,1,49]. For a recent survey, see [83].…”

“…Our method is also related to methods based on neighborhood agreement and votes as proposed in [66,101,98,49]. Also, in [1] the authors performed statistical tests (under Gaussian hypothesis) from pixels within sliding windows (see also [2,49]) as we also suggest ; in [4], the authors proposed a tracking algorithm ("Frag-Track") which combines multiple votes and histogram comparisons in spatial neighborhoods [4] ; in [15,16], the authors presented a generative and Bayesian method to detect unusual situations in an image sequence. Few examples on image pairs (visual inspection and defect detection) are reported in [16] but no objective comparison with existing change detection methods are given.…”

Vessel Segmentation in 2D-Projection Images Using a Supervised Linear Hysteresis Classifier

“…The simplest form of a linear hysteresis classifier working in a 1D feature space is a bi-threshold procedure called hysteresis thresholding [2,13,5,1]. Assuming that object points are described by high values of the feature and non-object points by low values, a high threshold has the role of the "pessimist" and selects only object-points and a low threshold is the "optimist" and selects all object-points.…”

“…Canny [2] recommends that their ratio should be between two and three. In [13,1] they are chosen in an applicationdependent way. In [5] they are set by hypothesis testing based on specific error probabilities (significance levels) for both high and low threshold.…”