2007/2008 The intensity of natural light can span over 10 orders of magnitude from starlight to direct sunlight. Even in a single scene, the luminance of the bright areas can be thousands or millions of times greater than the luminance in the dark areas; the ratio between the maximum and the minimum luminance values is commonly known as dynamic range or contrast. The human visual system is able to operate in an extremely wide range of luminance conditions without saturation and at the same time it can perceive fine details which involve small luminance differences. Our eyes achieve this ability by modulating their response as a function of the local mean luminance with a process known as local adaptation. In particular, the visual sensation is not linked to the absolute luminance, but rather to its spatial and temporal variation. One consequence of the local adaptation capability of the eye is that the objects in a scene maintain their appearance even if the light source illuminating the scene changes significantly. On the other hand, the technologies used for the acquisition and reproduction of digital images are able to handle correctly a significantly smaller luminance range of 2 to 3 orders of magnitude at most. Therefore, a high dynamic range (HDR) image poses several challenges and requires the use of appropriate techniques. These elementary observations define the context in which the entire research work described in this Thesis has been performed. As indicated below, different fields have been considered; they range from the acquisition of HDR images to their display, from visual quality evaluation to medical applications, and include some developments on a recently proposed class of display equipment. An HDR image can be captured by taking multiple photographs with different exposure times or by using high dynamic range sensors; moreover, synthetic HDR images can be generated with computer graphics by means of physically-based algorithms which often involve advanced lighting simulations. An HDR image, although acquired correctly, can not be displayed on a conventional monitor. The white level of most devices is limited to a few hundred cd/m² by technological constraints, primarily linked to the power consumption and heat dissipation; the black level also has a non negligible luminance, in particular for devices based on the liquid crystal technology. However, thanks to the aforementioned properties of the human visual system, an exact reproduction of the luminance in the original scene is not strictly necessary in order to produce a similar sensation in the observer. For this purpose, dynamic range reduction algorithms have been developed which attenuate the large luminance variations in an image while preserving as far as possible the fine details. The most simple dynamic range reduction algorithms map each pixel individually with the same nonlinear function commonly known as tone mapping curve. One operator we propose, based on a modified logarithmic function, has a low computational cost and contains one single user-adjustable parameter. However, the methods belonging to this category can reduce the visibility of the details in some portions of the image. More advanced methods also take into account the pixel neighborhood. This approach can achieve a better preservation of the details, but the loss of one-to-one mapping from input luminances to display values can lead to the formation of gradient reversal effects, which typically appear as halos around the object boundaries. Different solutions to this problem have been attempted. One method we introduce is able to avoid the formation of halos and intrinsically prevents any clipping of the output display values. The method is formulated as a constrained optimization problem, which is solved efficiently by means of appropriate numerical methods. In specific applications, such as the medical one, the use of dynamic range reduction algorithms is discouraged because any artifacts introduced by the processing can lead to an incorrect diagnosis. In particular, a one-to-one mapping from the physical data (for instance, a tissue density in radiographic techniques) to the display value is often an essential requirement. For this purpose, high dynamic range displays, capable of reproducing images with a wide luminance range and possibly a higher bit depth, are under active development. Dual layer LCD displays, for instance, use two liquid crystal panels stacked one on top of the other over an enhanced backlight unit in order to achieve a dynamic range of 4 ÷ 5 orders of magnitude. The grayscale reproduction accuracy is also increased, although a “bit depth” can not be defined unambiguously because the luminance levels obtained by the combination of the two panels are partially overlapped and unevenly spaced. A dual layer LCD display, however, requires the use of complex splitting algorithms in order to generate the two images which drive the two liquid crystal panels. A splitting algorithm should compensate multiple sources of error, including the parallax introduced by the viewing angle, the gray-level clipping introduced by the limited dynamic range of the panels, the visibility of the reconstruction error, and glare effects introduced by an unwanted light scattering between the two panels. For these reasons, complex constrained optimization techniques are necessary. We propose an objective function which incorporates all the desired constraints and requirements and can be minimized efficiently by means of appropriate techniques based on multigrid methods. The quality assessment of high dynamic range images requires the development of appropriate techniques. By their own nature, dynamic range reduction algorithms change the luminance values of an image significantly and make most image fidelity metrics inapplicable. Some particular aspects of the methods can be quantified by means of appropriate operators; for instance, we introduce an expression which describes the detail attenuation introduced by a tone mapping curve. In general, a subjective quality assessment is preferably performed by means of appropriate psychophysical experiments. We conducted a set of experiments, targeted specifically at measuring the level of agreement between different users when adjusting the parameter of the modified logarithmic mapping method we propose. The experimental results show a strong correlation between the user-adjusted parameter and the image statistics, and suggest a simple technique for the automatic adjustment of this parameter. On the other hand, the quality assessment in the medical field is preferably performed by means of objective methods. In particular, task-based quality measures evaluate by means of appropriate observer studies the clinical validity of the image used to perform a specific diagnostic task. We conducted a set of observer studies following this approach, targeted specifically at measuring the clinical benefit introduced by a high dynamic range display based on the dual layer LCD technology over a conventional display with a low dynamic range and 8-bit quantization. Observer studies are often time consuming and difficult to organize; in order to increase the number of tests, the human observers can be partially replaced by appropriate software applications, known as model observers or computational observers, which simulate the diagnostic task by means of statistical classification techniques. This thesis is structured as follows. Chapter 1 contains a brief background of concepts related to the physiology of human vision and to the electronic reproduction of images. The description we make is by no means complete and is only intended to introduce some concepts which will be extensively used in the following. Chapter 2 describes the technique of high dynamic range image acquisition by means of multiple exposures. In Chapter 3 we introduce the dynamic range reduction algorithms, providing an overview of the state of the art and proposing some improvements and novel techniques. In Chapter 4 we address the topic of quality assessment in dynamic range reduction algorithms; in particular, we introduce an operator which describes the detail attenuation introduced by tone mapping curves and describe a set of psychophysical experiments we conducted for the adjustment of the parameter in the modified logarithmic mapping method we propose. In Chapter 5 we move to the topic of medical images and describe the techniques used to map the density data of radiographic images to display luminances. We point out some limitations of the current technical recommendation and propose an improvement. In Chapter 6 we describe in detail the dual layer LCD prototype and propose different splitting algorithms for the generation of the two images which drive the two liquid crystal panels. In Chapter 7 we propose one possible technique for the estimation of the equivalent bit depth of a dual layer LCD display, based on a statistical analysis of the quantization noise. Finally, in Chapter 8 we address the topic of objective quality assessment in medical images and describe a set of observer studies we conducted in order to quantify the clinical benefit introduced by a high dynamic range display. No general conclusions are offered; the breadth of the subjects has suggested to draw more focused comments at the end of the individual chapters. XXI Ciclo 1982