**Geometry : Digital Vido and HD**

In mathematics, coordinate values of the (two-dimensional) plane range both positive and negative. The plane is thereby divided into four quadrants (see Figure 1.4). Quadrants are denoted by Roman numerals in the counterclockwise direction. In the continuous image plane, locations are described using Cartesian coordinates [x, y] – the first coordinate is associated with the horizontal direction, thee second with the vertical. When both x and y are positive, the location is in the first quadrant (quadrant I). In image science, the image lies in this quadrant. (Adobe’s Postscript system uses first-quadrant coordinates.)

In matrix indexing, axis ordering is reversed from Cartesian coordinates: A matrix is indexed by row then column. The top row of a matrix has the smallest index, so matrix indices lie in quadrant IV. In mathematics, matrix elements are ordinarily identified using 1-origin 1-origin indexing – in particular, MATLAB and Mathematica, both of which have deep roots in mathematics. The scan line order of conventional video and image processing usually adheres to the matrix convention, but with zero-origin indexing: Rows and columns are usually numbered [r,c] from [0,0] at the top left. In other words, the image is in quadrant IV (but eliding the negative sign on the y-coordinate), but ordinarily using zero-origin indexing.

Digital image sampling structures are denoted width x height. For example, a 1920 x 1080 system has columns numbered 0 through 1919 and rows (historically, “picture lines”) numbered 0 through 1079.

**Image capture : Digital Video and HD**

In human vision, the three-dimensional world is imaged by the lens of the eye onto the retina, which is populated with photoreceptor cells that respond to light having wavelengths ranging from about 400 nm to 700 nm. In video and in film, we build a camera having a lens and a photosensitive device, to mimic how the world is perceived by vision. Although the shape of the retina is roughly a section of a sphere, it is topologically two dimensional. In a camera, for practical reasons, we employ a flat image plane, sketched in Figure 1.5 above, instead of a section of a sphere. Inage science involves analyzing the continuous distribution of optical power that is incident on the image plane.