In this chapter, we shall look at the basic theory that underlies image formation and processing. We shall start by investigating what makes up a picture and look at the consequences of having a different number of points in the image. We shall also look at images in a different representation, known as the frequency domain. In this, as the name implies, we consider an image as a collection of frequency components. We can actually operate on images in the frequency domain and we shall also consider different transformation processes. These allow us different insights into images and image processing, which will be used in later chapters not only as a means to develop techniques but also to give faster (computer) processing.
The previous chapter covered finding shapes by matching. This implies knowledge of a model (mathematical or template) of the target shape (feature). The shape is the fixed in that it is flexible only in terms of the parameters that define the shape or the parameters that define a template’s appearance. Sometimes, however, it is not possible to model a shape with sufficient accuracy or to provide a template of the target as needed for the GHT. It might be that the exact shape is unknown or it might be that the perturbation of that shape is impossible to parameterize. In this case, we seek techniques that can evolve to the target solution or adapt their result to the data. This implies the use of flexible shape formulations. This chapter presents four techniques that can be used to find flexible shapes in images and these can be distinguished by the matching functional used to indicate the extent of match between image data and a shape. If the shape is flexible or deformable , so as to match the image data, we have a deformable template . This is where we shall start. Later, we shall move to techniques that are called snakes , because of their movement. We shall explain two different implementations of the snake model. The first one is based on discrete minimization and the second one on finite element analysis. We shall also look at determining a shape’s skeleton, by distance analysis and by the symmetry of their appearance. This technique finds any symmetric shape by gathering evidence by considering features between pairs of points. Finally, we shall consider approaches that use the statistics of a shape’s possible appearance to control selection of the final shape, called active shape models .
Over the recent few years, extensive research efforts have shifted from normal (n-i-p) to inverted (p-i-n) perovskite solar cells (PSCs), owing to their promising efficiency and operational stability, enabled by low-temperature processing. Despite a fundamentally identical operation principle (only structurally inverted), the optimized perovskite compositions for normal and inverted PSCs differ significantly across the literature, suggesting an underlying design principle for perovskite composition. Here, we unveil the role of cesium cation in enhancing interfacial contact between the perovskite layer and the underlying hole-transporting layer (HTL) in inverted PSCs. Comprehensive in situ and device characterization reveal that cesium incorporation promotes the formation of initial nucleation seeds for heterogeneous nucleation at the perovskite/hydrophobic HTL interface, thereby improving their contact. The resulting compositional heterogeneity explains the focus of recent studies on resolving this issue. This study provides mechanistic insight into designing perovskite compositions to further enhance the performance and longevity of PSCs.
Tomonaga-Luttinger liquid (TLL) behavior in one-dimensional systems has been predicted and shown to occur at semiconductor-to-metal transitions within two-dimensional materials. Reports of one-dimensional defects hosting a Fermi liquid or a TLL have suggested a dependence on the underlying substrate, however, unveiling the physical details of electronic contributions from the substrate require cross-correlative investigation. Here, we study TLL formation within defectively engineered WS_2 atop graphene, where band structure and the atomic environment is visualized with nano angle-resolved photoelectron spectroscopy, scanning tunneling microscopy and spectroscopy, and non-contact atomic force microscopy. Correlations between the local density of states and electronic band dispersion elucidated the electron transfer from graphene into a TLL hosted by one-dimensional metal (1DM) defects. It appears that the vertical heterostructure with graphene and the induced charge transfer from graphene into the 1DM is critical for the formation of a TLL.
Polymorphism in molecular crystals arises from the interplay between conformational strain, intramolecular forces, and collective lattice dynamics, yet its control remains largely empirical. Here, we show that deliberate molecular design that takes into account the dynamics of the constituent molecular building blocks programs polymorphic tendencies in molecular solids. A modular series of compounds that combine rigid aromatic cores with mobile imine linkers and rotatable tert-butyl moieties yields multiple thermally-accessible polymorphs with distinct low-energy vibrational signatures. Variable-temperature X-ray diffraction and low-frequency Raman spectroscopy reveal that each molecular design establishes characteristic low-frequency dynamics that correlate directly with macroscopic phase behavior. As more static motifs are introduced, the accessible low-energy coordinates contract and phase transitions become reversible, demonstrating that intramolecular design shapes the collective motions that accompany structural reorganization. Interestingly, the direct measurement of the low-frequency dynamics highlights that molecular motions are thermally-activated before the thermodynamic phase transitions, revealing internal motions that precede cooperative structural transformations. Together, these results provide a direct and designable connection between lattice dynamics and polymorphism, and that by tuning the motions of the molecular building blocks polymorphism can be effectively programmed. The principles established here are general, and can be extended to other chemical platforms to explore how vibrational energy landscapes are related to bulk dynamic phenomena.
