0.8 Signal processing in processing: miscellanea  (Page 3/5)

Histogram-based processing.

Image Histograms

Graphic representation by means of vertical bars, where each bar represents the number of pixels present in the image for a given intensity of the gray scale (or color channel). Wikipedia definition.

Among the examples in Processing , one finds the code Histogram that overlap an image to its own histogram.

The histogram offers a synthetic representation of images, in which one looses the information concerning the pixel positions and considers only the chromatic aspects. This provides information about the Tonal Gamma of an image (gray intensity that are present) and about the Dynamics (extension of the Tonal Gamma). The image of a chess board, for example, has a Tonal Gamma that includes only two gray levels (black and white) but it has a maximal dynamics (since white and black are the two extremity of the representable gray levels).

The histogram is the starting point for various processing effects aiming at balancing or altering the chromatic contents of an image. In general,the question is building a map $g_{\mathrm{o}}=f(g_{\mathrm{i}})$ for the gray levels (or color-channel levels) that can be applied to each pixel. The histogram can drive the definition of this map.

Translation and expansion of an histogram

If the map is of the kind $g_{\mathrm{o}}=g_{\mathrm{i}}+k$ the histogram is translated in the sense of a higher or lower brightness, according to the sign of $k$ . On the other side, if the map is of the kind $g_{\mathrm{o}}=k{g}_{\mathrm{i}}$ the histogram will be expanded or compressed, for values of $k$ smaller or greater than $1$ , respectively.

The contrast stretching is one of the operations of this kind of linear scaling that tries to extend the dynamic range of an image. The intervalby means of which one performs the scaling is set on the basis of the histogram, neglecting, for example, thetails of the distribution corresponding to $10\%$ of the darkest and brightest pixels.

Non linear scaling

More in general, the map $g_{\mathrm{o}}=f(g_{\mathrm{i}})$ can be non linear, and this allows a greater flexibility in the manipulation of the histogram. A usefulinstrument is the one that allows to manipulate interactively the scaling map and to see the results on the image and/oron the histogram in real time. The instrument Color Tools/Curves of the image processing software Gimp does this, using an interpolating spline. In Processing it is possible to build a similar instrument, as reported in [link] .

Equalization of an histogram

The non linear scaling is the tool to equalize the histogram, that is to shape it in a desirable way. An image has a balanced tonal gamma, if all of the gray levels arerepresented and if the distribution is approximately uniform. In other words, one aims at a flat histogram. Without entering too much into the mathematicaldetails, one can say that the non linear map to be used for the equalization is obtained from the cumulated distribution of the histogram of the image $f(g_{\mathrm{i}})=\sum_{k=0}^{g_{\mathrm{i}}} h(k)$ , where $h(k)$ is the frequency, properly scaled by means of a normalization constant, with which the $k$ -th gray level appears .