In this paper, we consider a task of stopping the video stream recognition process of a text field, in which each frame is recognized independently and the individual results are combined together. The video stream recognition stopping problem is an under-researched topic with regards to computer vision, but its relevance for building high-performance video recognition systems is clear. Firstly, we describe an existing method of optimally stopping such a process based on a modelling of the next combined result. Then, we describe approximations and assumptions which allowed us to build an optimized computation scheme and thus obtain a method with reduced computational complexity. The methods were evaluated for the tasks of document text field recognition and arbitrary text recognition in a video. The experimental comparison shows that the introduced approximations do not diminish the quality of the stopping method in terms of the achieved combined result precision, while dramatically reducing the time required to make the stopping decision. The results were consistent for both text recognition tasks.