What is zooming?

Zooming which is a digital image enlargement is accomplished for being used by some interpolation techniques. The purpose is to facilitate the visualization of the image through a resampled version.

It is used when a viewer needs another version of the original image but with more details or an easier form to perceive them.  This technique is extremely used in analysis and scientific visualization, as medical, aerial and spatial images; used for entertainment; application using digital still cameras. Consequently from an image I[n,n] is formed an X[an-1,an-1] that has an/2 pixels from I[n,n] e an/2 holes. The holes or nulls are filled by interpolation techniques.

Interpolation Techniques

All interpolation methods work in a fundamentally similar way as described above. In order to determine the value for an interpolated pixel we need to locate neighbors in the input image. The value is assigned from a weighted average of some set of pixels in the neighborhood of the point. The weights are proportional to the distance of each pixel from the point concerned.

Nearest-neighbor, bilinear, cubic and B-spline interpolation are conventionally methods proposed for image resampling [4,5,6,7]. The methods differ in the sets of the pixels that are considered:

1. Nearest Neighbor Interpolation: each interpolated output is assigned the value of the nearest pixel in the input image. It is a local interpolation using a finite number of the �nearest neighbor� candidates, which gives interpolated values that do not, in general, have continuous first or higher order derivatives.

2. Bilinear: each interpolated output is assigned the value of the weighted average of the four adjacent pixels, i.e. in the nearest 2-by-2 neighborhood. It is a combination of linear interpolation used in a two dimensional domain.

3. Cubic: each interpolated output is assigned the value of the weighted average on the sixteen adjacent pixels, i.e. in the nearest 4-by-4 neighborhood.

4.  B-spline: each interpolated output is assigned a value from a polynomial fitting. Polynomial coefficients are determined locally in order to assure global smoothness up to the highest order of the derivatives. Cubic B-splines are the most popular. They produce an interpolated function that goes on until the second derivative. B-splines of the order 0 and 1 coincide with the nearest neighbor and linear interpolants.

Other interpolation method is the non-linear, which deals with a non-linear transformation on the image which means we can not represent it as a linear function.

1. The linear interpolation takes correlation into consideration (LIC) it is a variation of a linear interpolation. The process involves using just one direction for interpolation, chosen by the correlation of color values. The direction with the highest correlation, i.e. horizontal or vertical, is chosen, and the other dimension is completely ignored locally. So, the undefined pixels receive the average of the two neighbors at the selected direction [8].

2. The linear interpolation which took the variance into consideration involves an 8-neighborhood formed by two concentric squares, in order to give more coherence to the interpolating decision nods; and compute the thresholds needed for edge direction based on the variance of the data. Those characteristics keeping edges and details while smoothing [2,3].

Interpolation Scheme

All methods create interpolated pixels into null positions, as (x₁,y_2...7).

My articles

The first one deals with edge-preserving, i.e. sensing the lightining direction in order to preserve details [1].
The latest creates a new interpolation scheme using a different neighborhood [2].