Useful Image Processing Methods. Useful Image Processing Methods. Noise Estimation Tangential Smoothing Variance Based Edge Strength

Introduction This document has been written to provide a description of some algorithms that are the frequently used in TINA [6], but would be considered too simple to be published. The common characteristic of these techniques is that they have relatively well defined statistical properties, allowing them to be used as useful intermediate stages in an image processing system. Motivation Many computer vision algorithms can be seen to have a large number of control parameters which are key to their successful application. These parameters tend to proliferate when constructing systems rendering the them unreliable for general use. In many cases these parameters are present in order to mitigate the effects of poor data and can be traced back to the effects of input image noise. Dealing with such issues in a satisfactory manner is made much easier if the input images and results of any processing stages have spatially uniform noise (σ I). Processed images can often be pre-processed by a non-linear transformation in order to obtain this property. Free parameters can then be eliminated, if some way can be found to relate them to a noise estimate. In some cases (such as thresholds for feature detectors such as Canny) this may be a simple proportionality. Pragmatic application of this strategy therefore requires a method for automatically estimating noise in an arbitrary image. Method (a) 0 σ (b) Figure 1: The noise is estimated from the variance of the distribution of second derivatives, following subtraction of uniform background. The method we prefer is based upon the observation that high order derivatives in images are dominated by the effects of image noise. Following this line of reasoning a histogram of the second order derivative from an image will illustrate two main features; a long tail of values associated with genuine image structure, and a peak at zero associated entirely with the noise process. The distribution of noise on a derivative of an image has a variance which is in a fixed proportion to the variance in the original image [3]. Measuring the width of the peak at zero thus provides a method for estimating the original image noise. This simple idea needs some care to make it work reliably in arbitrary images. 2 Two histograms are formed for the second derivatives in x and y. Valid derivatives are identified by eliminating any zero values adjacent to another zero value. This is …