Threshold operator

In principle, the algorithms for color constancy, which are described in the following chapters, can also be applied to the rotated coordinates (Figure 2.20). Land notes that, in practice, the transformation may not be that simple if the algorithm is nonlinear, i.e. contains a thresholding operation. We see later, e.g. in Section 6.6, Section 7.5, or Section 11.2, that some of the algorithms for color constancy are also based on a rotated coordinate system where the gray vector, i.e. the achromatic axis, plays a central role. 

Essentially, this operation computes the average reflectance ratio between the reflectance of the current point and the average reflectance of random samples surrounding the point (Brainard and Wandell 1992 Hurlbert 1986). If the threshold operation is used and the paths are assumed to pass through all of the image pixels then the retinex algorithm is simply normalization with respect to the response at the largest location (Brainard and Wandell 1992). 

Let us assume for a moment that the illumination is uniform, then the threshold operation is not needed. If we take the current point as a reference and consider multiple paths from the surrounding points that pass through the current point, we obtain... 

A threshold operator is used to separate these two components. Let (x) be a threshold operator... 

Laplacian, the result no longer resembles the input image. Results for Blake s version, which computes the first derivative, applies the threshold operation and then computes the second derivative instead of thresholding the output of the Laplacian, and are shown in Figure 7.16. By thresholding the first derivative, the Laplacian can still be inverted. The result is much more pleasing. 

Here e = k E/73, A = k2/73. So Eqs. (10a), (10b) and the corresponding equations for a2, p2 involve the depletion effect of the pump mode, which leads to the appearance of the above-threshold operational regime. 

We list below the semiclassical results for the stable values of photons number and phases of the modes. In the above-threshold operational regime at f th, where... 

When comparing the laser threshold energy values it is apparent that the most promising candidates for low-threshold operation are guest-host systems. Here, the self-absorption of the material matrix is effectively separated from the spectral region of the emission. The doped systems containing DCM2 or the stilbene... 

The threshold operation allows us to identify structures of interest that reasonably have a uniform brightness level, in general in an interval also known as the threshold range. 

The threshold operation is chosen in an interval with a heuristic method all the points inside this range assume the value of 1 (white) and the others the value 0 (black). 

In 1995, Zheng et al. (1995c) reported a multistage CAD scheme using a Gaussian band-pass filter and nonlinear threshold operation followed by a multilayer ANN to reduce the number of false-positively detected clusters. 

The selection of variables could separate relevant information from unwanted variability and at the same time allows data compression, that is more parsimonious models, simplification or improvement of model interpretation, and so on. Although many approaches can be used for features selection, in this work, a wavelet-based supervised feature selection/classification algorithm, WPTER [12], was applied. The best performing model was obtained using a daubechies 10 wavelet, a maximum decomposition level equal to 10, between-class/within-class variance ratio criterion for the thresholding operation and the percentage of selected coefficients equal to 2%. Six wavelet coefficients were selected, belonging to the 4th, 5th, 6th, 8th, and 9th levels of decomposition. 

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