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Feature analysis plays an important role in many multispectral image applications and scale invariant feature transform (SIFT) has been successfully applied for extraction of image features. However, the existing SIFT algorithms cannot extract features from multispectral images directly. This paper puts forward a novel algorithmic framework based on the SIFT for multispectral images. Firstly, with the theory of the geometric algebra (GA), a new representation of multispectral image including spatial and spectral information is put forward and discussed. Secondly, a new method for obtaining the scale space of the multispectral image is proposed. Thirdly, following the procedures of the SIFT, the GA based difference of Gaussian images are computed and the keypoints can be detected in the GA space. Fourthly, the feature points are finally detected and described in the mathematical framework of the GA. Finally, the comparison results show that the GA-SIFT outperforms some previously reported SIFT algorithms in the feature extraction from a multispectral image, and it is comparable with its counterparts in the feature extraction of color images, indicating good performance in various applications of image analysis. [ABSTRACT FROM AUTHOR]