Abstract: A spherical harmonic is defined which is an operationally optimal small finite subset of the infinite number of spherical harmonics allowed to exist mathematically. The composition of the subset differs depending on its position on virtual hemisphere. The subsets are further divided into small spherical tesserae whose dimensions vary depending on the distance from the hemispherical center. The images of the outside visual scenes are projected on the flat surface of the webcam and from there are read and recalculated programmatically as if the images have been projected on the hemisphere, rotational invariants are then computed in the smallest tesserae using numerical integration, and then invariants from neighboring tesserae are added to compute the rotational invariant of their union. Every computed invariant is checked with the library and stored there if there is no match. The rotational invariants are solely used for visual recognition and classification and operational decision making.

Abstract: A spherical harmonic is defined which is an operationally optimal small finite subset of the infinite number of spherical harmonics allowed to exist mathematically. The composition of the subset differs depending on its position on virtual hemisphere. The subsets are further divided into small spherical tesserae whose dimensions vary depending on the distance from the hemispherical center. The images of the outside visual scenes are projected on the flat surface of the webcam and from there are read and recalculated programmatically as if the images have been projected on the hemisphere, rotational invariants are then computed in the smallest tesserae using numerical integration, and then invariants from neighboring tesserae are added to compute the rotational invariant of their union. Every computed invariant is checked with the library and stored there if there is no match. The rotational invariants are solely used for visual recognition and classification and operational decision making.

Abstract: A spherical harmonic is defined which is an operationally optimal small finite subset of the infinite number of spherical harmonics allowed to exist mathematically. The composition of the subset differs depending on its position on virtual hemisphere. The subsets are further divided into small spherical tesserae whose dimensions vary depending on the distance from the hemispherical center. The images of the outside visual scenes are projected on the flat surface of the webcam and from there are read and recalculated programmatically as if the images have been projected on the hemisphere. rotational invariants are then computed in the smallest tesserae using numerical integration, and then invariants from neighboring tesserae are added to compute the rotational invariant of their union. Every computed invariant is checked with the library and stored there if there is no match. The rotational invariants are solely used for visual recognition and classification and operational decision making.

Abstract: A spherical harmonic is defined which is an operationally optimal small finite subset of the infinite number of spherical harmonics allowed to exist mathematically. The composition of the subset differs depending on its position on virtual hemisphere. The subsets are further divided into small spherical tesserae whose dimensions vary depending on the distance from the hemispherical center. The images of the outside visual scenes are projected on the flat surface of the webcam and from there are read and recalculated programmatically as if the images have been projected on the hemisphere. rotational invariants are then computed in the smallest tesserae using numerical integration, and then invariants from neighboring tesserae are added to compute the rotational invariant of their union. Every computed invariant is checked with the library and stored there if there is no match. The rotational invariants are solely used for visual recognition and classification and operational decision making.

Abstract: A new method of image processing and recognition through calculation of expansion of projected images onto a spherical coordinate system with at least two sets of presumed spherical harmonics defined on it with different positions of their North Poles, and subsequent computation of expansion coefficients of the images into the abovementioned orthogonal systems of spherical harmonics, and then calculating the invariants of images to rotational and translational transformations as vector and scalar products of two series of expansions. The invariants of the images will be stored in a magnetic library and subsequently used in image recognition in various industrial and security/military applications.