Tone Mapping

Tone mapping operators (TMOs) reduces an HDR image so that it can be rendered onto a LDR monitor in a manner that maintains the relative luminosities and reproduces the overall effect of the original scene, in a way that clamping effects occurring through the use of standard graphics output devices is avoided [DD02]. Within the past decade, researchers have developed many algorithms that will take a set of luminance values from a larger, unrestricted range to a much smaller, restricted range.

A good TMO could be described as one which produces an image that is perceptually similar to the original scene. Most of the algorithms operate on the luminance of an HDR image, since luminance largely governs our contrast perception [Aky12]. Tone mapping methods can either be global (also called spatially invariant) or combined with a local processing (also called spatially variant), modelling either only the global adaptation, or the global and local adaptation of the HVS.

3.4.1 Global Tone Mapping Operators

A global TMO uses a monotonic mapping curve to independently transfer real-world lighting and colour to the display. The algorithms apply the same function to all pixels of the image, that is one input value results in one and only one output value. For example, such a TMO can be a power function, a logarithm or a sigmoid curve across all values in the image of a functionf that is image-dependent [DBDQ10]. The goal is to approximate the HVS’s non-linearity,

to compensate for the display characteristics, or to render visually more appealing images. Global tone mappers tend to be more restricted in the aesthetic quality of the image they produce due to low levels of relative contrast between objects. Eilertsen et al [EWMU13] showed that a global strategy is, however, unable to capture important local transitions that may need to be preserved in order to maintain an overall level of local contrast corresponding to the original HDR input. In particular, logarithmic function have been applied in different ways [DMAC03] to luminance to increase contrast and brightness for the display of HDR images, on the low luminance values while compressing the higher luminance values.

Logarithmic TMO

A logarithm function is often used to approximate the non-linear encoding of the HVS. Thus, in the log-encoded image, equal steps in log-luminances correspond to equal visual sensations. This enables a perceptually uniform quantization where the perceived difference between two digital code values remains constant over the digital code value range. Such a logarithm function is used in the Retinex model of colour vision [EWMU13].

Gamma

Display devices have a non-linear relationship between input voltage and display luminance. This non-linearity is described by a power law and is commonly called gamma, which is referred to as the numerical value of the exponent. The output of a monitor can be modelled as follows:

L=Vγ _(3.3)

where V is the input voltage, γ is the gamma value of the display and L is the

In order to display corresponding luminance to those of the capture scene, the non-linearity has to be inverted. To achieve this, each colour channels of an input imageIis processed as follows:

I_c0 = I

1

γ

c (3.4)

where c denotes one of the RGB colour channels of the input imageI, and I0 is the gamma corrected image. Theγvalue depends on the monitor. A common average

value of gamma is 2.2.

On top of compensating for the display non-linearity, an advantage of gamma encoding is that it approaches the functions described above in a way that models the HVS non-linearity. Thus, a gamma-encoded image is also approximately perceptually uniform [KYJF04].

Gamma Correction with Adaptation on the Image Key

In addition to compensating for the output medium non-linearity, we may also want to improve the reproduction of an image depending on its content. An image can be characterised by its dominant tones, which is called the key. The key of an image indicates whether it is subjectively light, normal or dark, thus [KYJF04] approximated it by the log average luminance∧:

∧ =exp(1

N _p

∑

where p is a pixel in the image I whose luminance channel is given by ∧, N is the number of pixels, and∈ is a small value to avoid singularities caused by the presence of black pixels.

The gamma exponent value may be adapted to the key of the image to render more pleasing images. However, when rendering a low key image, it is

desirable to carry out gamma correction with a greater gamma value to improve detail visibility in dim areas.

3.4.2 Local Tone Mapping Operators

Local tone mapping algorithms apply different functions for different spatial pixel positions. Instead of applying the same tone curve to the entire image, they adapt each pixel individually based on the surrounding pixels. That means, one input value can result in more than one output value depending on the pixel position and on surrounding pixel values. Local TMOs consider pixel neighbourhood information in the mapping processing for each individual pixel, which simulates the adaptive and local property of colour vision called Retinex. The goal of Retinex is to recover the perceived colours from the captured scene radiances [MMK08]. They improve the quality of the tone mapped image over global operators by attempting to reproduce both the local and the global contrast. Local tone mappers regard the area around a given pixel in order to best utilise the available dynamic range, otherwise halos around edges can appear. However, Halos are sometimes desired when attention needs to be given to a particular area [BADC].

To preserve local contrast, Chiu et al [CHS∗93] proposed to preserve local contrast, where the TMO is used to scale the world luminance with neighbouring pixels average. This is defined as:

L_d(x) =Lw(x)s(x) (3.6)

s(x) is the function for scaling applied to compute the local average of the neighbouring pixels, which is defined as:

s(x) = (k(Lw⊗Gσ)(x))

−1 _(3.7)