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This paper presents novel homotopic image pseudo-invariants for face recognition based on pixelwise analysis. An exemplar face and test images are matched, and the most similar image is determined first. The homotopic image pseudo-invariants are calculated next to judge whether the most similar image is the same person as the exemplar. The proposed method can be applied to openset recognition. Recognition task can be performed with or without face databases, while the recognition rate is higher when a database is available. This fact facilitates the recognition of faces and various other objects on the Internet. We benchmark the method using FERET as well as the images downloaded from the Internet.