An algorithm for distinguishing and tracking multiple objects placed on a touchscreen has five steps. Step S1 is to find out candidate patterns from locations of touch points detected on the touchscreen, where the touch points are detected at a certain time instant. Step S2 is to discard invalid (i.e. overlapped) candidate patterns from the candidate patterns obtained in the step S1. Step S3 is to validate and update the geometry of each identified pattern. Step S4 is to update the attributes of identified patterns survived in the step S3. Step S5 is to forecast the geometry of patterns, and display the object. The steps S1-S5 are repeated for a next time instant. In executing the step S1 for the next time instant, the candidate patterns are excluded from any already identified pattern for reducing computation and storage required in executing the step S1.