Interval-Valued Model Level Fuzzy Aggregation-Based Background Subtraction

In a recent work, the effectiveness of neighborhood supported model level fuzzy aggregation was shown under dynamic background conditions. The multi-feature fuzzy aggregation used in that approach uses real fuzzy similarity values, and is robust for low and medium-scale dynamic background conditions such as swaying vegetation, sprinkling water, etc. The technique, however, exhibited some limitations under heavily dynamic background conditions, as features have high uncertainty under such noisy conditions and these uncertainties were not captured by real fuzzy similarity values. Our proposed algorithm is particularly focused toward improving the detection under heavy dynamic background conditions by modeling uncertainties in the data by interval-valued fuzzy set. In this paper, real-valued fuzzy aggregation has been extended to interval-valued fuzzy aggregation by considering uncertainties over real similarity values. We build up a procedure to calculate the uncertainty that varies for each feature, at each pixel, and at each time instant. We adaptively determine membership values at each pixel by the Gaussian of uncertainty value instead of fixed membership values used in recent fuzzy approaches, thereby, giving importance to a feature based on its uncertainty. Interval-valued Choquet integral is evaluated using interval similarity values and the membership values in order to calculate interval-valued fuzzy similarity between model and current. Adequate qualitative and quantitative studies are carried out to illustrate the effectiveness of the proposed method in mitigating heavily dynamic background situations as compared to state-of-the-art.