Series of methods for improved detecting and segmenting objects, situated on a complex background, have been developed. Model-based detection was applied for automatic detection and segmentation of the objects of interest on initial images and images after optimal filtering. The optimal linear filter was used to improve imaging of the object (its details and margin) on the observed image. Filtering of small-size details to improve false alarm and misdetection rates then followed the segmentation procedure. Developed series of methods were tested on test images and real medical images (lung tomograms) with small solitary nodules. A comparison of segmentation results obtained before and after optimal filtering showed that optimal filtering allows to outline the object region on medical images better and helps to identify more precisely the object margin. The developed series of methods can be useful for computer-assisted detection, segmentation, and analysis of low contrast flaws (lesions) on a complex image background that is important for solving of numerous medical tasks and for technical tasks of material inspection.