This is a widespread research area, and there have been numerous works that have been published in this field. While talking of face recognition, one assumes as given, that a face is what we are working with. In other words, it is somewhat a priori condition that the object of interest here is a face.

One must however understand that this is not the case always. Thus, we can look at the face recognition problem as a second layer problem, wherein the first would be to identify the fact from the given data. That is, if we are given a person's image, we first need to strike upon the face, and then go about identifying the person.

Face detection can be regarded as a specific case of object-class detection; In object-class detection, the task is to find the locations and sizes of all objects in an image that belong to a given class. Examples include upper torsos, pedestrians, and cars.

Face detection can be regarded as a more general case of face localization; In face localization, the task is to find the locations and sizes of a known number of faces (usually one). In face detection, one does not have this additional information.

Early face-detection algorithms focused on the detection of frontal human faces, whereas newer algorithms attempt to solve the more general and difficult problem of multiview face detection. That is, the detection of faces that are either rotated along the axis from the face to the observer (in-plane rotation), or rotated along the vertical or left-right axis (out-of-plane rotation),or both.

A given natural image often contains many more background patterns than face patterns. Indeed, the number of background patterns may be 1,000 to 100,000 times larger than the number of face patterns. This means that if one desires a high face-detection rate, combined with a low number of false detections in an image, one needs a very specific classifier. Publications in the field (including the two in this article's external links section) often use the rough guideline that a classifier should yield a 90% detection rate, combined with a false-positive (or type I error) rate in the order of 10-6. (Source: Wikipedia)

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Abstract algebra continues the conceptual developments of linear algebra, on an even grander scale.

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