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The techniques developed to deal with specular surfaces, either for detecting specularities or for extracting the object shape, must fulfill certain requirements, making them only viable in specific applications: for example, requirements related to specific electromagnetic characteristics of objects (i.e., specific methods for metallic or dielectric objects), having previous knowledge of the geometry of the scene or of the surface reflectance, etc.
To define our model, it is worth to remember the sensitivity as an important static characteristic of a sensor. The sensitivity is the slope of the calibration curve (see Figure 1). First, we can define the calibration curve as the function that maps a physical scene magnitude and its representation in the image space. Depending on the camera parameters the calibration curve will have a different function for different scene magnitudes. For instance, a camera with large depth of field will have a smoother calibration curve for intensity measurement (along a larger set of scene magnitudes for intensity, the camera will be able to distinguish between them) than a camera with short depth of field which will have a very abrupt calibration curve for the same scene magnitude (only a small set of intensity values will be distinguishable). With this function, sensitivity indicates the detectable output change for the minimum change of the measured magnitude. As a naive example, the detectable output could be the ability to perceive two different color that are actually different in the real scene. If the color change is too small, the sensor would return the same value of intensity. In our case, the detectable output in F for the minimum change of the scene magnitudes:
For the second alternative, Measurement Enhancement aims to directly influence the sensitivity curve of the acquisition system. In a nutshell, it tries to somehow highlight or enhance the parameters ρ which want to be perceived. It can be carried out by means of two new alternatives. First, the output signal of the perception system can be amplified. That is, the classic conception of measurement system amplification at the signal conditioning step. Limitations of this technique are related to increasing the amplitude of the signal in ranges of minimal sensitivity (both minimum and maximum of the range of the sensor because the contribution of the object in the output signal is insignificant, the signal-to-noise ratio is very low). In this way, acquisition system improvements are limited because they are only applied in ranges of intermediate sensitivity.
The set Δ Equation (20) is made up of lighting sources using the same characteristics (polarization, power, etc.) except the wavelengths, δi, to conform different spectral powers, Φδ. The wavelengths used are from the visible electromagnetic spectrum. Also, lighting sources only radiate for specific wavelengths (monochromatic lights).
In this paper, four different configurations of lighting are considered: two for spatial gradients (ξx and ξxy) and two for amplitude gradients (ξL and ξI). Regarding the former two, the function ξ establishes spectral powers of Δ Equation (20) into two different spatial distributions. Specifically, in the experiments the spatial gradient established by ξ is organized in one direction, ξx, and in two directions, ξxy, (see Figure 11). Let ROG(x, y) be the region of column x and row y of the lighting grid and let Nx, Ny be the column and row of neighbouring regions of the grid. A function ξ will be defined as ξx if it only sets up different lighting characteristics in adjacent positions of an axis of the grid (Figure 10a) and the same ones in adjacent positions of the other axis of the grid. Then, any region in the grid ROG is assigned an element of the set Δ such that:
It is interesting to consider the shape of the curve in Figure 13a. The graph represents the success rate of the system as a function of the scale. This is pixels per millimetre and not pixels per defect. The defects used in the tests have a maximum size of 0.6 mm for one of their three dimensions. Therefore, the scale values ρE correspond to 0.6, 1.2, 3, 6 and 9 pixels per dimension of the defect. For the minimum scale (1 pixel/mm), a crack or crater defect is projected into 0.28 pixels2 and a chromatic defect is projected into 0.36 pixels2. This corresponds to an area of 7.065 and 9 pixels2 respectively in the image of a defective plane (25 defects, see Figure 9). Then, the differences of 1 pixel in the image suppose that success rates vary 11.11% or 14.15%. The ratio of success rate to pixel is very large. Conditions for the next scale (2 pixels/mm) are similar. In this case, differences of 1 pixel in the image means the detection or not of a defect. The topographic defects are projected into an area of 1.13 pixels2 and the chromatic ones into an area of 1.44 pixels2. Differences of 1 pixel for the rest of the scale values mean a lesser impact on the detection.