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Multi-resolution approach to object detection wherein all entities including the partial information and background knowledge are modeled in set-theoretic terms whereby associated processing are formulated via set-theoretic operations is investigated. The generic set-theoretic paradigm is then applied to particular problems of detecting malfunctions in semiconductor fabrication process wherein the computational- and storage- efficiencies as enabled by morphological signal processing further coupled with flexibilities enabled by multi-resolution approach leads to a scalable paradigm in which the desired performance can be obtained on-demand fashion.