Abstarct: Image segmentation and detection of objects in pictures have always been important tasks in artificial vision. The segmentation of similar sections -or similar objects-between two pictures or a collection of pictures is called cosegmentation. The similar sections shall contain a rigid object, a non-rigid object, a scene, or similar objects of the same category. Objects can also be segmented from different viewpoints. Current paper studies background cosegmentation in which there are a number of similar backgrounds in picture collections though every picture contains a subset of the backgrounds. Because of the simpler assumption, this issue is in contrast to the classic cosegmentation problem in most available algorithms. Current study offers an optimal procedure for cosegmentation of multiple backgrounds that assigns no hypothesis on the backgrounds and surpasses limitations of previous procedures caused error. Current study used the same pattern which alternately runs a process of background modeling and a process of areal allocation modeling. These two processes both have a good optimality. The proposed algorithm, in general, is considered flexible enough for advanced categorization of any background or specified area through a complex selection procedure. The proposed algorithm offers several astonishing features as linear complexity and accuracy in detection.