Comprehensive evaluation of image enhancement for unsupervised image description and matching

IET Image ProcessingVolume 14, Issue 16 p. 4329-4339 Research ArticleFree Access Comprehensive evaluation of image enhancement for unsupervised image description and matching Michela Lecca, Corresponding Author Michela Lecca lecca@fbk.eu Fondazione Bruno Kessler (FBK), via Sommarive 18, Trento, 38123 ItalySearch for more papers by this authorAlessandro Torresani, Alessandro Torresani Fondazione Bruno Kessler (FBK), via Sommarive 18, Trento, 38123 Italy Department of Information Engineering and Computer Science, University of Trento, ItalySearch for more papers by this authorFabio Remondino, Fabio Remondino Fondazione Bruno Kessler (FBK), via Sommarive 18, Trento, 38123 ItalySearch for more papers by this author Michela Lecca, Corresponding Author Michela Lecca lecca@fbk.eu Fondazione Bruno Kessler (FBK), via Sommarive 18, Trento, 38123 ItalySearch for more papers by this authorAlessandro Torresani, Alessandro Torresani Fondazione Bruno Kessler (FBK), via Sommarive 18, Trento, 38123 Italy Department of Information Engineering and Computer Science, University of Trento, ItalySearch for more papers by this authorFabio Remondino, Fabio Remondino Fondazione Bruno Kessler (FBK), via Sommarive 18, Trento, 38123 ItalySearch for more papers by this author First published: 18 February 2021 https://doi.org/10.1049/iet-ipr.2020.1129AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Abstract The performance of an image enhancer is usually evaluated either perceptually or functionally. The perceptual evaluation is carried out from a human perspective, i.e. by considering features related to human perception of image content and details. The functional evaluation is made instead from a machine perspective, i.e. by judging the enhancer effects with a specific machine application. his work proposes a comprehensive, empirical evaluation accounting for both perceptual and functional aspects. Precisely, 13 enhancers lowering undesired illumination effects are considered within the keypoint based image description and matching task, which is relevant to many computer vision fields. Each enhancer is first evaluated perceptually, then it is employed as a pre-processing step of the popular algorithms SIFT and ORB and judged by measuring how its use influences the performance of these algorithms. his study, conducted on a freely available data set, shows that the enhancement generally improves the perceptual features of the input image as well as the SIFT and ORB performance. More importantly, it reveals the existence of a correlation among some of their perceptual and functional measures. In this way, this work contributes to promote a more aware use of enhancement techniques within the mage description and matching task. 1 Introduction Image enhancers are computer vision algorithms that improve the local and global visibility of an input image. They achieve this task by processing one or more image features so that the enhanced image is brighter, more contrasted and smoother than the input one, while possible chromatic dominants and shadows due to the light are lowered. The features and the computational model used to improve the visibility of the image content vary from enhancer to enhancer, mainly depending on the image typology (e.g. medical, real-world, marine, aerial, etc.) and on the final purpose for which the enhancer is invoked. In this respect, the enhancers are often employed as a pre-processing step of other algorithms that require as an input high quality visual data. The evaluation of the performance of an image enhancer is a hard, open problem since there are no agreed methodologies for this task [[1]]. Searching on the net for expressions like 'image enhancement assessment' often brings to subjective or objective measures, which basically judge the enhancer based on its capability to make a picture more pleasant and readable for humans [[1]-[3]]. Subjective measures quantify human judgements of the visibility of the image content and thus they are irredeemably biased by personal aesthetic issues that even may lead to conflicting results. Objective measures usually analyse the numerical amount and variations of few human perceptual features of the image before and after the enhancement or with respect to a 'perfect' a-priori model. Since the perceptual features concurring to the image quality are still not yet fully understood, the perceptual (i.e. perception-based) measures provide an incomplete picture of the enhancement level. In addition, both the subjective and objective measures completely ignore the impact that the enhancement may have on computer vision tasks not related to the human perception. In this respect, a machine-oriented functional evaluation, i.e. an assessment carried out from the perspective of the algorithm that makes use of the enhancer, is of great interest. Such an evaluation provides indeed a context-based, objective, not necessarily and exclusively perceptual information about the enhancement level, while enables an aware usage of the enhancement method that is the most adequate for the application at hand, e.g. [[4]-[7]]. Nevertheless, the functional evaluation often neglects the perceptual cues and their relationship with the machine vision application. Here, we provide a comprehensive assessment of image enhancement taking into account both perceptual and functional aspects. Specifically, in this work we evaluate 13 image enhancers (i) perceptually by comparing the brightness, the contrast, the entropy and the regularity of the input and output images, and (ii) functionally, within the task of unsupervised description and matching of real-world colour images. We focus on this application because it is strongly relevant to many modern machine vision applications like robot navigation, autonomous driving, virtual reality, 3D reconstruction, which need image descriptors robust against different conditions, in particular to low-light, multiple lights, light colour casts. With this purpose in mind, we consider here 13 enhancers that improve the image content by removing such light effects, while we do not cope with specific techniques for image denoising like, e.g. transform domain filtering and wavelet thresholding [[8]-[10]]. Our evaluation is empirical and consists of four steps. First, we apply an enhancer to a real-world colour image and we evaluate it by objective measures. Second, we input the enhanced image to an image description and matching algorithm. Third, we quantify the enhancer performance by comparing the description and matching results achieved with and without enhancement. Finally, we implement a multi-variate analysis to study how the perceptual changes are related to the functional performance. The enhancers we consider are representative of different methodologies for improving the visibility of the image content. They include methods exploiting statistical information, such as histogram equalisation and [[11], [12]], Retinex inspired spatial colour processing, i.e. [[13]-[17]], illuminance/reflectance decomposition [[18]-[20]] and machine learning techniques [[21]-[23]]. For image description and matching we consider the well known Scale Invariant Feature Trasform (SIFT) [[24]] and Oriented Fast and Rotated Brief (ORB) [[25]]. This choice is motivated by their wide usage in many computer vision applications, e.g. 3D reconstructions and robot navigation [[26]-[29]]. Moreover, SIFT and ORB offer two different kinds of image description models (floating point for SIFT, binary for ORB), that have inspired many other description and matching techniques, e.g. [[30]-[34]], many of which propose optimised or more robust versions of ORB and SIFT [[35]]. The contributions of this work to the state-of-the-art are manifold. First, our assessment paves the way for a new class of enhancer evaluation methods. In fact, it judges the enhancement level both from a human and a machine vision perspective, and investigates the existence of a correlation between a set of widely used perceptual measures and the performance of the enhancer in a given application context. Second, our evaluation enables a more aware use of image enhancers in the specific machine vision field of image description and matching with particular attention to the case of multi-exposure and low-light images. Finally, since the images used for testing our approach and their enhanced versions are publicly available, our work grants the repeatability of the results as well as further comparisons and studies. 2 Image enhancement Let us introduce some notation used in the next. Let I ¯ be a colour image with size N × M and let I be one of its intensity channels. Here, I is regarded as a map from S : = = { 1 , … , N } × { 1 , … , M } to the set { 0 , … , 255 } and I ( x ) denotes the intensity value of any pixel x with spatial coordinates ( r x , c x ) ∈ S. The colour of x is denoted by I ¯ ( x ) which indicates the triplet ( I 0 ( x ) , I 1 ( x ) , I 2 ( x ) ) of the red, green and blue intensity values at x. The set S is referred as the support of I and the length of its diagonal is indicated by D. The Euclidean distance between the spatial coordinates of two pixels x and y is denoted by ∥ x − y ∥. 2.1 Statistic approaches without illuminance/reflectance decomposition The statistic approaches described here are the histogram equalisation (HE), the Contrast Limited Adaptive HE (CLAHE) [[11]] and the global Quantile-Based approach to Retinex (QBRIX-g) [[12]]. All these enhancers process the channels of I ¯ separately and map any value I ( x ) onto a new value determined by analysing the distribution of I locally or globally. HE maps I ( x ) on the value L HE ( x ) = floor ( 255 ∑ i = 0 I ( x ) h ( i ) )(1) where h is the probability density function (pdf) of I. CLAHE implements a similar mapping, but replaces h with the pdf of I computed over a patch around x and introduces a threshold, called clipping limit, on the height of the pdf entries in order to avoid over-enhancement and noise amplification that may be produced by the histogram stretching. QBRIX-g re-scales the value I ( x ) by as follows: L QBRIX − g ( x ) = I ( x ) max ( q , I ( x ) ) (2) where q is the intensity value corresponding to a quantile Q of the pdf of I input by the user. When Q = 1, then QBRIX-g behaves like scale-by-max, i.e. the pixel intensities are re-scaled by the maximum intensity value over the image support. In general, for the most applications, 0.90 ≤ Q ≤ 0.99. 2.2 Milano-Retinex algorithms The Milano-Retinex algorithms [[36]] are spatial colour algorithms widely used for image enhancement. According to Retinex theory, they process the channels of I ¯ separately and map I ( x ) onto a value L ( x ) called lightness and obtained as follows: L ( x ) = I ( x ) w ( x ) (3) where w ( x ) > 0 is called local reference white and is computed by processing the intensity values of a set of pixels spatially sampled around x, in some case along with additional information like position and gradient magnitude [[37]]. In order to enable the intensity division, I is re-worked to be always strictly greater than zero, e.g. the intensity values equal to zero are mapped to a positive value ε close to zero. The Milano-Retinex algorithms differ to each other in the way the pixels contributing to the image enhancement are sampled and in the equation of w ( x ). Here we consider three algorithms: Light-RSR [[13]], GREAT [[14]] and SuPeR [[16]]. Light-RSR (from light random spray Retinex) samples the neighbourhood of each pixel x by a random spray, i.e. a set S ( x ) of pixels randomly chosen with a radial density around x. The enhanced value L ( x ) is the ratio between I ( x ) and the maximum intensity over S ( x ). This ratio is blurred by box filters to lower possible chromatic noise due to the random sampling. GREAT and SuPeR replace the random sampling with a deterministic procedure. For each channel I, GREAT (from the key-words Gradient and Retinex) computes the set of high magnitude gradients Σ = { y ∈ S : ∥ ∇ I ( y ) ∥ ≥ τ }, where τ is a positive, real-valued threshold. Then for each pixel x ∈ S, GREAT computes the set Σ ′ ( x ) = { y ∈ Δ Σ : I ( y ) > I ( x ) }, where Δ Σ denotes the one-pixel dilation of Σ. Finally, GREAT computes w ( x ) as follows: w G ( x ) = ∑ y ∈ Σ ′ ( x ) ( 1 − ∥ x − y ∥ D ) ∥ ∇ I ( y ) ∥ I ( y ) ∑ y ∈ Σ ′ ( x ) ( 1 − ∥ x − y ∥ D ) ∥ ∇ I ( y ) ∥ if Σ ′ ( x ) ≠ ∅ I ( x ) otherwise (4) Therefore, the lightness output by GREAT depends on the gradient magnitude and on the position of the relevant edges with respect to x. The algorithm SuPeR is a simplified version of the Milano-Retinex approach STAR [[15]]. STAR introduced a novel computational framework, where the information relevant to the lightness is extracted from super-pixels instead of from neighbourhoods recomputed pixel by pixel. The super-pixels of STAR are the regions obtained from a segmentation of I. To cut down the computational burden of STAR and remove the dependence of the enhancement performance on the segmentation algorithm, SuPeR considers a regular partition of S in m tiles B 1 , … , B m , where m is input by the user. Each tile is then treated as a regular super-pixel extracted from a regular grid, from which the name. SuPeR processes the tiles to compute the set B = { y 1 , … , y m } where, for any i = 1 , … , m, y i is the maximum intensity over B i . Then, for each pixel x SuPeR defines the set B ( x ) = { y i ∈ B : I ( y i ) > I ( x ) } and computes the value of w ( x ) by these conditions: w S ( x ) = ∑ y i ∈ B ( x ) 1 − ∥ b i − x ∥ D ∑ y i ∈ B ( x ) 1 − D − 1 ∥ b i − x ∥ I ( y i ) if B ( x ) ≠ ∅ I ( x ) otherwise (5) where b i is the centre of mass of B i for any i = 1 , … , m. 2.3 Luminance remapping Firefly [[17]] is a tool for the adjustment of the local image brightness. It takes as input an RGB image, converts it to the YUV colour space, and map each pixel RGB triplet ( I 0 ( x ) , I 1 ( x ) , I 2 ( x ) ) onto a new triplet ( I 0 ′ ( x ) , I 1 ′ ( x ) , I 2 ′ ( x ) ) such that I i ′ ( x ) = Y ( x ) Y ′ ( x ) I i ( x ) ∀ i = 0 , 1 , 2(6) where Y ( x ) : = 0.299 I 0 ( x ) + 0.587 I 1 ( x ) + 0.114 I 2 ( x ) is the luminance at x and Y ′ ( x ) is the corresponding adjusted value of Y ( x ). This latter is modelled through a polynomial function Y ′ ( x ) = ∑ i = 0 n ∑ j = 0 n i + j ≤ n a i j Y i ( x ) m j (7) where m ranges over {0, …, 255} and describes the intensity around x, while a i j are weighting parameters. For each triplet ( Y , m , Y ′ ), the value of m is learned from a set of images along their versions processed by a given and well performing enhancer. The a i j 's are estimated through a fitting procedure over the triplets ( Y , m , Y ′ ). The method is hardware friendly because it runs on real-time and the fitting procedure can be performed on a space with reduced dimension without affecting the final results. 2.4 Illuminance/reflectance decomposition The Low-light image enhancement via Illumination Map Estimation (LIME) [[18]], the Naturalness Preserved Enhancement Algorithm for non-uniform illumination estimation (NPEA) [[19]] and the fusion-based enhancing method for weakly illuminated images [[20]] (here denoted by as FUSION) improve the content of a colour image I ¯ by removing its illumination component. These methods are based on the image formation model representing I ¯ as the product of the reflectance R of the material composing the acquired scene and the scene illumination I, i.e.: I ( x ) = R ( x ) I ( x ) ∀ x ∈ S .(8) Since R and I correspond, respectively, to the high- and low-frequencies of I ¯ , discarding I from I ¯ enables to remove smooth, unessential details while retaining the most significant image features. Nevertheless, recovering R and I from I ¯ is in general an ill-posed problem, that can be solved only in constrained domains. NPEA, LIME and FUSION starts from a coarse estimation I e of I at each pixel x(i.e. I e ( x ) = max i = 0 , 1 , 2 I i ( x )) and refine it according to some constraints that enables the solution of the illumination/reflectance decomposition problem. Precisely, NPEA assumes that the reflectance is limited to a specific range of values and that the local relative order of the image illumination values, defining the naturalness of the scene, changes slightly over adjacent regions. Within these hypotheses, NPEA refines I e ( x ) by convolving it with a bright-pass filter centred at x and accounting for the neighbouring values higher than the central one only. This convolution is followed by a bi-logarithmic transformation that reshapes the illumination map to simultaneously highlight the details while preserving the naturalness. The enhanced image is thus obtained as the product of the reflectance for the estimated illumination. LIME refines I e ( x ) by solving the following variational problem: min I ( ∥ I e − I ∥ F + α ∥ W ∇ I ∥ 1 )(9) where ∥ ⋅ ∥ F and ∥ ⋅ ∥ 1 are, respectively, the Frobenius and the l 1 norms, W is a matrix of weight and ∇ T is the gradient of I, while α is a parameter balancing the two terms. By this way, we observe that LIME assumes that the final illumination is close to the estimate I e ( x ) (first term) and smooth over the image (second term). The enhanced image is obtained as the pixel-wise ratio between the components of I ¯ and the estimated illumination. FUSION improves I e by applying sequentially a morphological and a guided filter. Indicated with I 1 the new estimate of I, FUSION derives from I 1 two new images I 2 and I 3 that are, respectively, the arctangent of I 1 and the version of I 1 enhanced by CLAHE. The final estimate of the illumination results from a multi-level, smoothed fusion of the three images I 1 , I 2 and I 3 that are summed up along with specific weights. The enhanced image is obtained as the pixel-wise ratio of the image I and the illuminant estimation, where of course division by zero is prevented. 2.5 Machine learning methods Image enhancement can be viewed as an optimisation problem, where an input image has to be transformed to maximise the visibility of its content while minimising artefacts and noise. In this framework, machine learning offers interesting solutions by modelling such maximisation/minimisation through the loss function of a neural network. Here we review three recent machine learning methods: the Multi-Branch Low-Light Enhancement Method (MBLLEN) [[23]], the Deep Retinex Decomposition of Low-Light Enhancement (RetinexNET) [[22]] and the Deep Light Enhancement without Paired Supervision (EnlightenGAN) [[21]]. MBLLEN implements a deep convolutional neural network composed by multiple subnets whose outputs are fused together. The main network consists of three computational modules: (i) a feature extraction module (FEM) consisting of a single stream network with ten convolutional layers devoted to the extraction of multi-level visual features; (ii) an enhancement module (EM) composed by ten subnets each of them taking as input a layer of the FEM and performing convolution and de-convolution operations; (iii) a fusion module (FM) merging together the results of the EM subnets. MBLLEN requires a paired data set of low-light/well-lighted images as training set and its loss function accounts for structural and visual differences between an image and the corresponding enhanced version. The structural differences are measured by SSIM [[38]] and MS-SSIM [[39]] and they are computed locally and globally, while the visual differences are based on features extracted through a VGG network [[40]]. RetinexNET [[22]] applies sequentially two neural networks called, respectively, Decomp-Net and Enhance-Net. Decomp-Net is a deep network that decomposes any image in reflectance and illumination and outputs its illumination map. Decomp-Net is based on three assumptions, that are modelled by the loss function: given a pair of low-light and normal images I L and I N , (i) I L and I N share the same reflectance; (ii) both the illumination maps of I L and I N are smooth and preserve the global structure of the acquired scene; (iii) the reflectance of the scene can be recovered both from I L and I N . For any image, Decomp-Net returns an estimation of its illumination map. This latter is then improved by the Enhance-Net through a multi-scale analysis, exploiting convolutional layers to make the illumination map consistent with the global and local image structures. RetinexNET denoises the estimated illumination map by smoothing artefacts and irrelevant details erroneously amplified by the enhancement process. It is to note RetinexNET does not need for a ground-truth of decomposed reflectance and illumination images, but only for a data set of paired low-light/normal-light images. One of the main issues to be addressed in machine learning is the availability of a sufficiently large and accurate data set of paired images to be used as a training set. EnlightenGAN [[21]] overcomes this problem by means of a generative adversarial network (GAN), that learns to enhance an image from unpaired low-light and normal-light/enhanced images from different domains. Basically, EnlightenGAN implements an attention guided U-Net [[41]] to compute local and global image features. Due to the absence of paired images, the net is equipped with a generator of data and with a discriminator module evaluating the quality of the generated data and rejecting those without realistic appearance. The loss function of EnhightenGAN measures the local and global similarities between the VGG features [[40]] extracted from the input-low image and from its enhanced version output by the generator after discrimination. 3 Key-point-based image description and matching Given a set of different images, the goal of image description and matching algorithms is to identify reliable and highly-discriminative pixel patterns enabling the associations of the images having common contents. SIFT and ORB pursue this task on grey-level images by two steps: (a) detection of key-points, i.e. the detection of pixels with discontinuous gradient (corners) in a multi-scale fashion; (b) description of the key-points, i.e. the computation for each key-point of a vector (i.e. the descriptor) encoding visual information of a patch around the key-point. Both ORB and SIFT match image key-points by comparing a similarity measure between their descriptors. In the implementation considered here, given two images Q and R, any key-point k of Q is matched against all the key-points of R and is associated to the key-point h of R whose descriptor has the maximum similarity to the descriptor of k. 3.1 Scale invariant feature transform – SIFT Let I be a grey scale image. SIFT computes a pyramid composed by groups of images, called octaves, at multiple scales. Each octave includes a set of versions of I each of them blurred by a Gaussian filter with increasing variance. Given the scale s, the adjacent images in the same octave are pixel-wise subtracted obtaining the so-called difference of Gaussians. The key-points of I at the scale s are defined as the local extrema in the space of the Gaussian differences. Precisely, the extrema is a pixel p whose intensity is brighter or darker than all the pixels located in a 3D neighbourhood of 26 elements around p. Extrema located on edges and/or having low-contrast are discarded since they do not provide a stable description. Each key-point K is described by a vector of 128 elements, encoding the local distributions of the gradient orientations from a 16 ×16 window centred at K. To achieve invariance against image rotation, each descriptor is steered according to the dominant (i.e. most frequent) orientation of the pixels around the corresponding key-point. Any key-point is thus defined by the quadruple < p , s , o , d >, where p is the image location at the scale s, o is the dominant orientation and d is the descriptor. The dissimilarity between two key-points is measured by the L 2 distance between their descriptors. 3.2 Oriented FAST and rotated BRIEF – ORB ORB combines and extends the FAST feature detector and the binary descriptor BRIEF, enabling invariance against changes of scale and/or perspective. A key-point of FAST is defined as a pixel p whose intensity exceeds by a given threshold t the intensities of the pixels lying on a circumference centred at p and with radius r. ORB performs this key-point extraction at multiple scales and computes the orientation θ ( K ) of any key-point K as the angle between the location of K and the centroid of a patch around K. This orientation is used to steer the BRIEF descriptor, which originally is not rotation invariant. BRIEF describes each key-point K located at a pixel x by a bit-string d of length n d , in which each element is the outcome (0 or 1) of n d comparisons of I ( x ) with the intensities of a smoothed patch around K. d is finally rotated by the angle θ ( K ) to achieve robustness against in-plane rotation. In the ORB implementation, the rotated BRIEF descriptor is a bit-string of 256 elements, and the dissimilarity between two key-points is measured by the Hamming distance of their descriptors. 4 Experiments 4.1 Data set We conduct our perceptual and functional evaluation of image enhancers on the data set MEXICO-2020, that we collected and made freely available along with its enhanced versions [https://drive.google.com/file/d/1QrpBA2pBMJ6hpGDPibjcFBEF1ragUjn5/view?usp=sharing]. MEXICO-2020 consists of 50 scenes of indoor and outdoor environments each represented by 6 images taken with exposure time T regularly increasing from 6 to 27 ms (see Fig. 1 for example). These images contain several challenges for both enhancement and retrieval tasks, such as difficult light conditions due to low- and back-light, shadows, illuminant colour casts, different textures and co-existence of bright and dark regions at different proportions. For testing the performance of ORB and SIFT, we have taken the images captured with the highest exposure time as references, while the others as queries. This choice is motivated by the fact that for each scene, the image acquired at T = 27 ms is that with the most uniform brightness distribution and with the higher detail visibility. Fig. 1Open in figure viewerPowerPoint Scene from MEXICO-2020 represented by six images acquired with increasing exposure time 4.2 Evaluation measures In the following we describe the perceptual and functional measures used in our evaluation. 4.2.1 Perceptual evaluation The perceptual evaluation has been carried out by comparing the following measures computed on any image and on each enhanced version of it: Mean brightness (b): Any colour image I ¯ is converted to a grey-scale image G by averaging pixelwise its R, G, B components; we define b as the mean value of the intensities of G. Mean multi-resolution contrast (c) [[42]]: This contrast, whose behaviour proved to be in line with that reported by humans, is computed on a pyramid of sequentially half-scaled versions of G, let's say G 1 , … , G v . For each i = 1 , … , v, the contrast c i ( x ) of a pixel x of G i is defined as the mean value of the L 1 distances between G i ( x ) and the intensity values of the 8 pixels surrounding x. The contrast of G is the average of the c i ( x )'s, and c is the average of the contrast of the G i 's. Histogram flatness (f ): Given the pdf H of the intensities of G, the flatness of H is its L 1 distance from the uniform pdf over the set {0, …, 255}: the lower f, the more uniform the pdf of G is. Image naturalness (NIQE) [[43]]: This value captures the regularity of the image I ¯ and it is related to its smoothness, measured through second-order statistics over I ¯ : the higher the NIQE the lower the image regularity is. An enhancer is expected to increase the brightness of I (i.e. b) and its detail visibility (i.e. c), to smooth or remove picks in the colour distribution (i.e. to decrease f ), while preserving or increasing the image naturalness (i.e. preserving or decreasing NIQE). As already noted in previous works, e.g. [[15]], the exact amount of b, c, f and NIQE and their variations after enhancement depend on the image content. In particular, for an already bright (dark, resp.) image with good (poor, resp.) detail visibility, low (high, resp.) variations of b, c, f and NIQE will be reported. In general, checking only one perceptual feature does not allow a reliable assessment of the enhancer. In fact, making an image completely white surely increases its mean brightness but does not improve the contrast, that is instead completely lost: in this case, the value of f will be high, indicating a poor performance of the