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Several applications of this is text recognition (OCR), face recognition (biometrics), camera guided missiles (targetting systems). Each involves analyzing images and making out some object of interest. Is there a term that describes this branch of programming?

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I'd use umbrella term for such a diverse field: Computer Vision (alternatively Machine Vision). –  MaR Sep 21 '12 at 16:39
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That's exactly it - computer vision, and the Wikipedia article has a lot of information about the subject. Calling it a branch of programming doesn't quite do it justice. –  Daniel B Sep 21 '12 at 17:06

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You're looking for Computer Vision:

...a field that includes methods for acquiring, processing, analyzing, and understanding images and, in general, high-dimensional data from the real world in order to produce numerical or symbolic information, e.g., in the forms of decisions. A theme in the development of this field has been to duplicate the abilities of human vision by electronically perceiving and understanding an image. This image understanding can be seen as the disentangling of symbolic information from image data using models constructed with the aid of geometry, physics, statistics, and learning theory...

As a scientific discipline, computer vision is concerned with the theory behind artificial systems that extract information from images. The image data can take many forms, such as video sequences, views from multiple cameras, or multi-dimensional data from a medical scanner...

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