Análisis interno y externo de cada proceso del departamento de Recurso humano

The illumination invariant image obtained is a function of both material reflectance and an unknown illuminant that is common for all pixels. In order to develop such a representation, each pixel needs to be multiplied by an appropriate scaling factor based on its original incident illumination properties.

For a pixel B0 occluded from the sun, assuming indirect illumination is negligible and

there is no emission, the radiance can be described by:

LB0(λ) =

ρB0(λ)

π [ΓB0Esky(λ)]. (3.4)

In order to relight the point with respect to skylight (denoted by LB0_−relit(λ)), the

radiance LB0(λ) needs to be multiplied by a scaling factor:

LB0_−relit(λ) = ρB0(λ) π [Esky(λ)], (3.5) = ρB0(λ) π [Esky(λ)] " ΓB0 ΓB0 # , = LB0(λ)  ₁ ΓB0  . (3.6)

The scaling factor in this case is purely geometric and independent of wavelength. Therefore, multiplication by this scaling factor will not influence spectral shape, only

its intensity.

For a pixel C that is exposed to terrestrial sunlight, the relit radiance can also be found by multiplying the original observed radiance by a scaling factor:

LC−relit(λ) = ρC(λ) π [Esky(λ)], (3.7) = ρC(λ) π [Esky(λ)] "

Esun(λ)τ (λ) cos αC + ΓCEsky(λ)

Esunτ (λ) cos αC + ΓCEsky(λ) #

,

= LC(λ)

"

Esky(λ)

Esun(λ)τ (λ) cos αC + ΓCEsky(λ)

# , = LC(λ)   1 Esun(λ)τ (λ) Esky(λ) cos αC + ΓC  , (3.8)

where the terrestrial sunlight-skylight ratio is known from the selection of a pair of points along a shadow boundary and Equation (3.3). The scaling factor in this case is wavelength dependent and must be applied on each spectral channel independently. This means that errors in the calculation of the terrestrial sunlight-skylight ratio will negatively affect the relighting process. These errors may arise due to an incorrect assumption of diffusivity, negligible indirect illumination or no emitted radiance. Therefore, Equations (3.6) and (3.8) show that all pixels can be relit to using a common illumination source (skylight), through the calculation of scaling factors per pixel. As an example of the effectiveness of the algorithm, Figure 3.3 presents the results obtained by relighting Dataset 7 using the relighting algorithm. Dataset 7 presents a complex scene structure, whose image is captured by a consumer grade RGB camera under clear sky conditions. There is no ground truth data available in this scene, so only qualitative evaluation may be performed. In order to apply the relighting equations to a consumer grade RGB camera, each channel is treated as having a Dirac delta sensor response and linear images are used.

The relit image is obtained using the full sky factor calculation and demonstrates that a high degree of spatial illumination invariance is achieved when compared to the original image. This is seen by comparing Figures 3.3c and 3.3d, which are regions of uniform material in the original and relit image highlighted by the red

   

(a) Original image.

   

(b) Relit image.

(c) Cropped region of uniform ma-

terial from the original image.

(d) Cropped region of uniform ma-

terial from the relit image. Figure 3.3 – Relighting Dataset 7, captured using a consumer grade RGB camera

under clear sky conditions. The regions highlighted by the red circles indicate regions of approximately uniform material exposed to different amounts of illumi- nation. Relighting the image is seen to increase the spatial illumination invariance properties of the image.

circles in Figures 3.3a and 3.3b respectively. The intensity and colour of the brown brick varies in the original image as one side of the building is occluded from the sun. Through relighting, all sides of the building appear similarly coloured and of equal intensity, thereby indicating higher spatial illumination invariance. Some artefacts are noticeable in the relit image, such as bright blue colours on the edge of the roof and front of the building. This is due to errors in the calculation of the surface normal, leading to the incorrect scaling factor being applied during relighting.

because only the non-occluded scaling factor is wavelength dependent. The scaling factor for the occluded region is a constant, which is advantageous as these regions typically have a low SNR. If they were to be multiplied by a wavelength dependent scaling factor (as is the case when relighting with respect to full exposure to sunlight and skylight as shown in Appendix B) it would amplify the noise, especially in the case of hyperspectral imagery. This is compared to consumer grade cameras which integrate spectral noise through the use of a wideband sensor response for each colour channel.

The drawback of using skylight as the common illuminant is that the resultant image will have a lower dynamic range than the original image. However, the relit image can be linearly scaled without loss of invariance, so this does not pose a problem. Compared to the shadow compensation method of [29], the proposed approach does not require the selection of a known number of materials under different illumina- tion conditions. This selection is required as optimisation is used to estimate both

the terrestrial sunlight-skylight ratio, and the function ρ(λ)Esky(λ) for each selected

material. The resultant relit image amplifies noise at longer wavelengths, while the proposed method does not have this property since relighting is performed with re- spect to the weaker illumination source.

A second advantage of the method presented in this thesis is that it does not require the use of highly parametrised atmospheric models such as MODTRAN [5] whose parameters are not available at all locations, and only needs a single image compared to the multiple image requirement of [79]. The state of the art illumination invariant image generation method of [25] has recently been applied to robotics applications [13], however this suffers from the fact that it loses the discriminative information of colour once it projects down to a single dimension [80] and also amplifies noise [51]. The proposed method retains the full spectral dimensionality of the original data and keeps noise amplification to a minimum.