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Calibration curve (red) and sensitivity (green) for the visual acquisition system (VAS) including tuning ρ s and working point ρ t .
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The use of visual information is a very well known input from different kinds of sensors.
However, most of the perception problems are individually modeled and tackled. It is necessary to
provide a general imaging model that allows us to parametrize different input systems as well as
their problems and possible solutions. In this paper, we present...
Contexts in source publication
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... 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. ...
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... a given camera c has maximum sensitivity for a value of each ρ i . For convenience, we are going to define the tuning point as the corresponding point ρ s in the scene magnitudes space P for each camera of the set Γ in which the sensitivity of the VAS is the optimum (see Figure 1) . The sensitivity decreases in general for values of ρ differently from ρ s . ...
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... object could be distinguishable from another one in the VAS when they are distinguishable in the measurement performed in F (i.e., in the vertical axis of Figures 1 and 2A). Let Ω m i be the set of objects that can be distinguished for an specific object m i , and let χ the minimum difference perceptible by the system (sensitivity), then Ω m i could be established as: ...
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... VAS has to deal with different situations that are a consequence of the subsets of P delimited by the problem to be solved (e.g., delimited by objects or by their characteristics to be analysed, or by environments, or by the cameras, etc.). A minimum value of sensitivity χ can be established in which any object is distinguishable from another considered in the acquisition (see Figure 1). The values of the vector of magnitudes ρ in which sensitivity is higher than a threshold χ conform the subset S of P defined by Equation (8). ...
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... solutions have to be provided to achieve distinct images from different objects that the camera perceives as the same one. These solutions should be able to compensate the low sensitivity in S c (sensitivity less than χ in Figure 1). Among the three variables that provide values to the scene magnitudes, object is a constant due to them being the subject of interest. ...
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... lighting characteristics of the set ∆ are distributed over each of the regions ROL determined by s establishing different gradients: spatial and amplitude. In the experiments, for practical considerations, the ROG composed of a squared grid has been used (Figure 10). In this paper, four different configurations of lighting are considered: two for spatial gradients (ξ x and ξ xy ) and two for amplitude gradients (ξ L and ξ I ). ...
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... the former two, the function ξ establishes spectral powers of ∆ Equation (20) into two different spatial distributions. Specifically, in the experiments the spatial gradient established by ξ is organized in one direction, ξ x , and in two directions, ξ xy , (see Figure 11). Let ROG(x, y) be the region of column x and row y of the lighting grid and let N x , N y be the column and row of neighbouring regions of the grid. ...
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... ROG(x, y) be the region of column x and row y of the lighting grid and let N x , N y be the column and row of neighbouring regions of the grid. A function ξ will be defined as ξ x 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 ∆ such that: ...
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... the second spatial gradient, a function ξ will be defined as ξ xy if sets up different lighting characteristics in all adjacent positions of a region of the grid (Figure 10b). Any region in ROG is assigned to an element of the set ∆ Equation (20) such that: Regarding the amplitude gradients, two configurations are also considered for ξ: Linear, ξ L , and Interlaced, ξ I . ...
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... region in ROG is assigned to an element of the set ∆ Equation (20) such that: Regarding the amplitude gradients, two configurations are also considered for ξ: Linear, ξ L , and Interlaced, ξ I . A function ξ will be defined as ξ L if sets up lighting characteristics with close wavelengths in adjacent positions N of the regions of the lighting grid ROG (see Figure 11a) whereas the Interlaced, ξ I , configuration maximize the differences among wavelengths in these positions (see Figure 11b). Then, in case of ξ L , any region in ROG is assigned to an element of the set ∆ Equation (20) such that: ...
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... region in ROG is assigned to an element of the set ∆ Equation (20) such that: Regarding the amplitude gradients, two configurations are also considered for ξ: Linear, ξ L , and Interlaced, ξ I . A function ξ will be defined as ξ L if sets up lighting characteristics with close wavelengths in adjacent positions N of the regions of the lighting grid ROG (see Figure 11a) whereas the Interlaced, ξ I , configuration maximize the differences among wavelengths in these positions (see Figure 11b). Then, in case of ξ L , any region in ROG is assigned to an element of the set ∆ Equation (20) such that: ...
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... case of any function that is considered as an Interlaced function, ξ I , the ROG is assigned such that: Figure 11. Amplitude distribution considered for function ξ in the experiments. ...
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... X' and Interlaced X are made up using the function ξ x establishing 120, 60, 40 and 20 ROLs according to the areas of the regions considered. Figure 12 shows the different lighting patterns used in the experiments. Figure 12. ...
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... 12 shows the different lighting patterns used in the experiments. Figure 12. Samples of lighting patterns generated by the transformation υ Φ used in the experimentation. ...
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... study of the perception scale makes discerning the influence of the size of the defects in the image possible. Figure 13a shows the success rates according to the dielectric object. The function 'Interlaced XY' offers the best success rates whereas the 'Linear X' offers the minimum of the transformations Υ Φ . ...
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... differences in success rates according to metallic object are more noticeable (see Figure 13a). The function 'Interlaced XY' shows similar success rates to the case of dielectric material. ...
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... 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. ...
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... success rates of the different transformations Υ Φ according to the perception angle ρ θ are shown in Figure 13c,d, for the dielectric and metallic objects respectively. ...
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... the intensity lighting ρ I as the angle formed by surface normal and lighting plane normal, the success rates of the different lighting configurations are shown in the Figure 13e,f, for the dielectric and metallic objects respectively. The function 'Interlaced XY' provides the maximum success rate and the greatest increase in the capacity of perception of the system. ...
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... influence of the size of the lighting regions ROL defined by s on the capacity of perception according to the scale is indicated on the left of Figure 14 and according to the angle on the right of the Figure 14. The size of ROL is represented by the minimum dimension of the region. ...
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... influence of the size of the lighting regions ROL defined by s on the capacity of perception according to the scale is indicated on the left of Figure 14 and according to the angle on the right of the Figure 14. The size of ROL is represented by the minimum dimension of the region. ...
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... average differences vary from 4% to 5% in the scale case. According to angle, the average differences are about 7% for the crack defect (Figure 14e) in the interval of the maximum sensitivity [10 • , 40 • ]. The behaviour for the crater defect ( Figure 14d) is analogous; it establishes an average difference of sensitivity in that interval of 5%. ...
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... to angle, the average differences are about 7% for the crack defect (Figure 14e) in the interval of the maximum sensitivity [10 • , 40 • ]. The behaviour for the crater defect ( Figure 14d) is analogous; it establishes an average difference of sensitivity in that interval of 5%. The differences decrease as the perception angle increases until they are 0 for 90 • . ...
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... analysis of the chromatic defect shows that the size of lighting regions is independent of the success rate (see Figure 14c,f). In this case, it is practically constant. ...
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... inspection conditions are restricted to only 5 values of the scene magnitudes ρ i for a metallic object with an unstructured lighting (reference lighting). As can be seen in Figure 15 The choice of the conditions (scale, angles, etc.) to capture the whole object for inspection is a complex problem. It is necessary to take into account the particularities of each solution. ...
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... consequence, in order to apply the results, any point on the surface can be viewed as a point on a plane whose normal vector is the normal of the surface at that point. For example, Figure 16a shows an outline of this assumption. In this way, the surface can be analysed as a set of planes (a plane per point on the surface). ...
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... scale will be determined by the number of pixels available to the sensor by setting the camera position at a focus distance and at a constant focal length. The conditions of the angle of perception will be established by the movement on the X and Y axis of the origin of coordinates located in the center of the of the object: the Yaw and Pitch movements of the camera (see Figure 16b). Due to select the variables is a complex problem, an approximation to the optimum solution is proposed in order to determine the appropriate angles between camera and object surface. ...
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... logo inspection requires 26 captures (see Figure 17a and Table 4) using the lighting reference and a camera of 1452 × 1452 pixels to acquire a surface area of 4619.96 mm 2 (98.79% of the logo). ...
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... captures can be made using a lower resolution of up to 510 × 510 pixels. According to the function 'Interlaced XY', only 9 images are necessary (see Figure 17b and Table 5). The camera resolution varies between 826 × 826 and 1455 × 1455 in order to cover a total surface area of 4675.05 mm 2 (99.9%). ...
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