Supplementary material

Ophtalmic and Physiological Optic

Volume 30, Issue 5, 2010, pp. 492-502

Spatially coherent colour image reconstruction from a trichromatic mosaic with random arrangement of chromatic samples

David Alleysson

Laboratory of Psychology and NeuroCognition (LPNC), CNRS UMR 5105

Grenoble, France

January 2010

Matlab Code

Test Image

 
Figure S7

Figure S7: The construction of a mosaiced image from a colour image. (a) Colour image (b) Multiplication of each colour channel with the corresponding chromatic mosaics that contain the position of each colour receptor. (c) Colour representation of the mosaiced image (d) Achromatic representation of the mosaiced image.

Figure S7 illustrates the construction of a mosaiced image with randomly arranged color receptors from a colour image. A colour image is composed of three chromatic channels C_i, i in {R, G, B}, we can thus write a colour image as a vector of three components I(x,y) = {C_R(x,y), C_G(x,y), C_B(x,y)}. We construct three random matrices called m_R, m_G and m_B, which are used to define the arrangement of the colour samples in the mosaic. These modulation matrices m_i(x,y) are binary, they contain value 1 at spatial position (x,y) if the receptor of type i is present at that position or 0 if the receptor is missing. Thus, the subsampling matrices, S_R, S_G and S_B of each chromatic channel is given by the multiplication (element per element) of the chromatic channel C_R, C_G and C_B with the modulation matrix, S_i = C_i.m_i, i in {R, G, B}. For the Red channel, for example, we can write: S_R = C_R.m_R.

By combining these subsampled channels, we can construct a colour image composed of vectors with three values at each spatial position. Two components of these vector are equal to zero, only one value, either R, G, or B, is non-zero (Figure S7-c). However, this image is not a simulation of the cone mosaic image because we cannot assume that the position of each cone type is known by the visual system at the level of cones. Rather, we propose that the input image in the retina is the image in Figure 7S-d. This image represents the simulation of the cone mosaic without knowing which cone type is present at which particular spatial position. This image is a scalar image having only a single value per spatial position. It is formally defined as, Im =sum_i(C_i.m_i)= S_R+S_G+S_B and can be represented in greyscale.

Figure S8

Figure S8: Decomposition of a mosaiced image in space and Fourier domain. (a) Colour mosaic of a the image. (b) The achromatic part of the mosaiced image (c) The chromatic part of the mosaiced image, which is subsampled compared to Figure 3(b). The bottom figures are the modulus of the spatial Fourier transform of each top figure, processed as scalar images in greyscale.

Figure S9

Figure S9 : Schema of the “Chrominance First” method (Chaix de Lavarène, 2008 ; Alleysson et al., 2009). (a) Mosaiced image. (b) The low-frequency achromatic information estimated from the mosaic. (c) Horizontal and vertical scene contours estimated from the low frequency image. (d) Medium and high frequencies calculated from the difference between the mosaiced image and the low frequency achromatic information. (e) Demultiplexed image. (f) Chromatic interpolation under consideration of the the contour images.

Figure S9 illustrate the reconstruction of colour images from the trichromatic mosaics by the “Chrominance First” method. The method reconstructs chromatic information before achromatic information. The main idea is to perform a low frequency estimation of achromatic information from the mosaic using a low pass filter with low cut-off frequency (Supplement Figure S9-b) . This estimation is partial because only low frequency information is estimated.

Once the low spatial frequencies are estimated, it is possible to apply directional gradient filters (Figure S9-c). Even though not all the frequencies are available, the directional gradient can be estimated and thus scene regions where the main directions are horizontal, vertical, or both can be identified.

The difference image between the mosaic and the low spatial achromatic frequency is shown in supplementary Figure S9-d. This image contains the medium and high frequency bands of the achromatic information plus the full frequency band of the chromatic information, which is modulated. By demultiplexing this image, we separate the chromatic information and obtain subsampled colour (Figure S9-e). An interpolation procedure driven by the horizontal and vertical gradient images allows interpolating the chromatic channels with good accuracy (Figure S9-f).

The complete colour image reconstruction uses the chrominance (Figure S9-f) and luminance. For luminance, we combine the low frequency image (Figure S9-b) plus the difference of the images Figure S9-e and Figure S9-f. Figure S9-e contains both the high frequency of the achromatic information plus all frequencies of the chromatic information. Thus, by removing the interpolated chrominance (Figure S9-f), only the high frequencies of the luminance remains.

Figure S10

Figure S10 : Reconstruction with a packed cone arrangement. (a) Original image. (b) Image sampled with a uniform random arrangement. (c) Reconstruction from (b). (d) Image sampled with a packed arrangement. (e) Image reconstruction from (d).