Statistical distributional approach for scale and rotation invariant color image retrieval using multivariate parametric tests and orthogonality condition

• Proposed system retrieves texture and structure images, and invariant for scaling and rotation.
• Statistical distributional approach such as multivariate parametric tests are used.
• Test for equality of covariance matrices, and test for equality of mean vectors are employed.
• Canberra distance is used to compare the features: CV, Skw, Kur, VaCov, SoE, and number of shapes.
• Sum of product of position vectors is used to test the similarity of the query and target images.

This paper proposes a unified framework for color image retrieval, based on statistical multivariate parametric tests, namely test for equality of covariance matrices, test for equality of mean vectors, and the orthogonality test. The proposed method tests the variation between the query and target images; if it passes the test, then it proceeds to test the spectrum of energy of the two images; otherwise, the test is dropped. If the query and target images pass both the tests then it is concluded that the two images belong to the same class, i.e., both the images are same; otherwise, it is assumed that the images belong to different classes, i.e., both the images are different. The obtained test statistic values are indexed in ascending order and the image corresponds to the least value is identified as same or similar images. Here, either the query image or target image is treated as sample; the other is treated as population. Also, some other features such as Coefficient of Variation, Skewness, Kurtosis, Variance–Covariance, spectrum of energy, and number of shapes in the images are compared between the query and target images color-wise. Furthermore, to emphasize the efficiency of the proposed system, the geometrical structure, viz. test for orthogonality between the query and target images, is examined. In the case of structure images, the number of shapes in the query and target images are compared; if it matches, then the contents in the shapes are compared color-wise. The proposed system is invariant for scaling, and rotation, since the system adjusts itself and treats either the query image or the target image is the sample of other. The proposed framework provides hundred percent accuracy if the query and target images are same, whereas there is a slight variation for similar, scaled, and rotated images.