Читать книгу Diatom Morphogenesis - Группа авторов - Страница 33

Each SEM was taken at 0° stage angle. However, the diatom itself may be tilted or slanted in the stub mountant that may be present between the diatom and stub or sputter-coated medium that covers or infiltrates the diatom or other regions of the stub. Because of this, digital images need to be corrected for tilt and slant. Tilt and slant are measured via the gradient of the pixel gray-levels in each image. Tilt is the amount of change of the normal to a 0° plane or direction of slant [2.135], while slant is the angle of rotation different from the 0° plane [2.20]. The gradient measures the greatest amount of change in x- and y-directions over the entire image. Often, image changes are most evident at the boundaries or edges between objects or as changes in luminosity or gray scale value. This feature and the image pixel gray scale values contain information so that tilt and slant may be expressed as entropy values. The information contained in the digital image is measurable as the gradient entropy.

For an image with a range of pixel values, r, . Tilt, the angular direction that changes most within the image plane, is the gradient direction given as .Slant, the angular distance (in degrees) change out of the image plane, is the gradient magnitude given as The gradient entropies of the image, Sx-direction and Sy-direction , are used in the calculation of tilt and slant.

The angular difference between tilt and normal to the x-y plane can be corrected by a shear transformation [2.140] with respect to the y-z plane. That is, pixel position in the original image is transformed via a tangent function of tilt to new pixel positions. After masking and prior to rotation, each image is corrected for tilt in this way. Angular rotation out of the x-y plane is used to correct slant by using n-rotations. That is, image rotation in the image preparation process is used to correct for slant.