In the single view camera geometry it is not possibleto resolve the ambiguity of depth of the scene pointfrom its image point even with a calibrated camera,whose projection matrix is known. It is onlypossible to construct the ray in the 3-dimensional(3-D) world coordinate system passing through theimage point from the center of the camera. But in anoptical image a viewer can distinguish the objectpoint which forms the image. It is the opticalenergy received from that point in a surface of theobject and their distribution over its neighborhoodthat provide the key information to a viewer ininterpreting the object point and judging thedistances from the camera. In this chapter, wediscuss how the depth ambiguity in a single viewcamera geometry can be resolved with the help ofanother additional camera. The combined setup of twocameras is called stereo camera setup and thegeometry defined by them is referred to as stereo geometry.

12.1 | Epipolar geometry

A stereo setup consists of two cameras and a scenepoint, 𝑿, whose image is captured by the cameras,as illustrated in Fig. 12.1. The first (left) andthe second (right) cameras are specified by theircamera centers, 𝑪 and 𝑪′, respectively, whichcapture the images of the scene point on theirrespective image planes. In convention, the firstcamera or left camera is considered as the referencecamera of the stereo setup. By the rule ofprojection, let the image of the scene point, 𝑿, inthe first camera be 𝒙. Similarly, the image of 𝑿in the image plane of the second camera isrepresented by 𝒙′. The two images, 𝒙 and 𝒙′,correspond to the same scene point, 𝑿. Thus, forevery scene point, there will be two image points inthe image planes of the two cameras, if the scenepoint is visible from both the cameras.

Content based imageretrieval (CBIR) is a search techniquethat uses similarity of visual features to compareimages. It is also known as image based searchprocess, where, given a query image (with or withoutan accompanying text), the system provides a set ofimages that are similar to the query. This provisionis made available in most of the search engines,which enable us to search through the internet usinga query image and get several images that arerelevant to the query. The CBIR system has a lot ofapplications in various sectors, like education,research, tourism, health care, remote sensing, etc.In CBIR systems, while retrieving the resultsagainst a query, some domain specific information,like keywords, may also be provided to improve thequality of retrieval. The scope of such retrievalsystems could be extended to videos and multimediadocuments, which include text, audio, video,graphics, and images, as well.

Challenges and issues in building a CBIRsystem

Developing efficient CBIR systems is hurdled by severalchallenges. The image similarity computed forretrieving relevant images may not always satisfythe user's search intent. Often, objective criteriamay not fill the semantic gap in the representationof similar images. Some images, that are similar tohuman understanding, may be outright rejected asdissimilar images by a computational model. Manyobjective models are sensitive to noise and thepresence of a few outlier features may disturb thedecision by rejecting seemingly similar images oraccepting dissimilar images. In such cases ofsimilarity, thesystem does not explain why a pair of images aresimilar. Such sparingly occurring instances may beacceptable in some domains, but there are variousareas, like medicine and health care, where theverdict of a system is not acceptable without aproper explanation. Also, two images may be globallysimilar or they may have some local similaritybetween them. Capturing and localizing the localsimilarities for declaring a match between twoimages are also challenging. However, most of theCBIR systems work on global similarity.

Intensity images are limited in capturing surfacegeometry. Range imaging refers to an aggregation oftechniques to capture the surface topology as acollection of points that represent depths usingdifferent kinds of range sensors. Range images forma special class of digital images that requiredifferent processing techniques in their analysis.This chapter provides an overview of range imagingand processing.

13.1 | Range image

A range image is a 21/2-D or 3-D representation of the scene. It issometimes called 21/2 -D representation because itcaptures only the surface information of an objector scene as discretized points to represent it as animage. A range image, 𝑓(𝑖, 𝑗), records thedistance, d, to the corresponding scene point at(𝑥, 𝑦, 𝑧) for each image pixel, (𝑖, 𝑗), asshown in Fig. 13.1. In the array representation of arange image, the pixel values correspond to thedistances of the surface points, unlike conventionalRGB camera image pixels that represent intensities.The distribution of all the recorded values of dforms the functional distribution of the surfacepoints over the discretized space of the image,which is known as range data or depth data. Thisdepth information may also be represented as a setof 3-D scene points, also called a point cloud. Fora given functional value, 𝑓(𝑖, 𝑗), of an imagearray at an index position of (𝑖, 𝑗), thecorresponding pixel value of a scene point (𝑥, 𝑦,𝑧) in the discrete 3-D space is represented as (𝑖,𝑗, 𝑓(𝑖, 𝑗)). An example of a range image isshown in Fig. 13.2, where the intensity image iscaptured as an RGB color image and its correspondingrange image is captured using Microsoft™ Kinectsensor.

Solid mechanics, compared to mechanics of materials or strength of materials, is generally considered to be a higher level course. It is usually offered in higher semester to senior students. There are many textbooks available on solid mechanics, but they generally include a large part of theory of elasticity with in depth mathematical formulations. The usual prerequisites are one or two semester course on elementary strength of materials and a thorough mathematical background, including scalar, vector, and tensor field theory and cartesian and curvilinear index notation. The difference in levels between these books and elementary texts on strength of materials is generally formidable. However, in our experience of teaching this course for many years at premier institutes like IIT Kharagpur and Jadavpur University, despite its complexity, senior students generally cope well with the course using the readily available textbooks.

However, there is a vast student population pursuing mechanical, civil, or allied engineering disciplines across the country in colleges where AICTE curriculum is followed. Through several years of interaction with this group of students, we have found that there is no suitable textbook that suits their requirements. The book is primarily aimed at this group of students, attempting to bridge the gap between complex formulations in the theory of elasticity and elementary strength of materials in a simplified manner for better understanding. Index notations have been avoided, and the mathematical derivations are restricted to second-order differential equations, their solution methodologies, and only a few special functions, such as stress function and Laplacian operators.

The text follows more or less the AICTE guidelines and consists of twelve chapters. The first five chapters introduce the engineering aspects of solid mechanics and establish the basic theorems of elasticity, governing equations, and their solution methodologies. The next four chapters discuss thick cylinders, rotating disks, torsion of members with both circular and noncircular cross-sections, and stress concentration in some depth using the elasticity approaches. Thermoelasticity is an important issue in the design of high-speed machinery and many other engineering applications. This is dealt with in some detail in the tenth chapter. Problems on contact between curved bodies in two-dimensional and three-dimensional situations can be challenging, and they have wide applications in mechanical engineering such as in bearing and gear technology.

Key Concepts

• • Steps involved for developing sustainable organizations

• • Case study on a university campus

• • Integration of green sources of energy

• • Implementation of energy efficiency measures

• • Ensuring participation of stakeholders for energy conservation

Introduction

The achievement of SDGs defined under the Paris Agreement requires concerted efforts at the international, national, state, organization, and individual levels. The organizations which follow the principles of sustainable development can serve as a role model for others to follow.

Colleges for higher education and the universities also have an important role to play in achieving the SDGs in general and in the adoption and promotion of green sources of electricity in particular. Goal 4 of SDGs, although, is specific to the availability of quality education to all, but these institutions can play a much broader role in realizing the wide-ranging SDGs. For example, Goal 9: Industry, infrastructure and innovation; Goal 12: Responsible production and consumption; and Goal 13: Climate Action cannot possibly be achieved without the mindful and positive influence of higher education institutions.

More importantly, these institutes need to work on the creation of awareness about the need for sustainable development and SDGs, a crucial requirement for their achievement. The institutes should also make sustainable development an integral part of their future plans. Green and renewable sources of energy like solar PV should be adopted for existing buildings, and these should be made mandatory for the new buildings. The academic institutes, more importantly, should practice on their campuses what they are preaching in the class.

Key Concepts

• " Working of solar PV power plants and their benefits

• " Different configurations of solar PV systems, such as grid-connected, stand-alone, and hybrid solar PV plants

• " Metering mechanisms, such as net metring and gross metring

• " Working and classification of different types of inverters used in solar energy generation

• " Different performance evaluation parameters for solar PV power plants and effect of environmental conditions

• " Components used in solar PV power plants

• " Challenges related to the large-scale integration of solar PV plants with the power grid

Introduction

Solar energy is a renewable source of energy, and when electricity is produced from solar, it does not lead to any CO2 emissions. Apart from being a green and renewable source of energy, solar is the simplest system of electricity generation. As described by Professor Martin Green, ‘The whole photovoltaic technology itself is a bit magical. Sunlight just falls on this inert material and you get electricity straight out of it.’ This technology has emerged as the most powerful solution for decarbonizing the energy system.

The solar PV plants can be installed in two modes: grid-connected and off-grid system. At present, grid-connected solar PV (GCSPV) plants are the most commonly used systems. Although solar PV cells, were discovered in the year 1953, solar PV plants for generating electricity did not gain widespread acceptance primarily because of the panel cost as well as the issues with the batteries involved. GCSPV technology has removed the weak link, the battery from the system, making it an efficient, economical, and durable system with minimum maintenance requirements. These benefits have made the solar PV the fastest rising system in the world.

3.1 STATE OF STRESS AT A POINT [LO1]

When a body is subjected to external forces, its behavior depends on the magnitude and distribution of forces and properties of the body material. Depending on these factors, the body may deform elastically or plastically, or it may fracture. The body may also fail by fatigue when subjected to repetitive loading. Here we are primarily interested in elastic deformation of materials.

In order to establish the concept of stress and stress at a point, let us consider a straight bar of uniform cross-section of area A and subjected to uniaxial force F as shown in Figure 3.1. Stress at a typical section A - A′ is normally given as σ = F/A. This is true only if the force is uniformly distributed over the area A, but this is rarely true. Therefore, definition of stress must be considered by progressively reducing the area until it is small enough such that the force may be considered to be uniformly distributed.

To understand this, consider a body subjected to external forces P1, P2, P3, and P4 as shown in Figure 3.2. If we now cut the body in two pieces,

Internal forces f1, f2, f3, etc. are developed to keep the pieces in equilibrium. Now consider an infinitesimal element of area ΔA Dat the cut section and let the resultant force on the element be Δf.

Introduction

A current mirror is a transistor-based circuit that the current level is controlled in an adjacent transistor, and the adjacent transistor essentially acts as a current source. Such circuits are now considered a commonly used building block in a number of analog integrated circuits (IC). Operational amplifiers, operational transconductance amplifiers, and biasing networks are examples of such circuits that essentially use current mirrors. Analog IC implementation techniques such as current-mode and switched-current circuits use current mirrors as basic circuit elements.

A significant advantage associated with the current mirrors is that they act as a near-ideal current source while fabricated using transistors and can replace large-value passive resistances in analog circuits, saving large chip area.

The later part of the chapter discusses another important analog circuit, namely, differential amplifier. As the name suggests, differential amplifiers amplify the difference between two signals that are applied to their two inputs. In addition to the differential amplification, it is also required that differential amplifiers suppress unwanted signal, which is present on the two input signals in the form of a common-mode signal. A differential amplifier is a particularly very useful and essential part of operational amplifiers. A differential pair is the basic building block of a differential amplifier that comprises of two transistors in a special form of connection.

This chapter presents the matrix deviation inequality, a uniform deviation bound for random matrices over general sets. Applications include two-sided bounds for random matrices, refined estimates for random projections, covariance estimation in low dimensions, and an extension of the Johnson–Lindenstrauss lemma to infinite sets. We prove two geometric results: the M* bound, which shows how random slicing shrinks high-dimensional sets, and the escape theorem, which shows how slicing can completely miss them. These tools are applied to a fundamental data science task – learning structured high-dimensional linear models. We extend the matrix deviation inequality to arbitrary norms and use it to strengthen the Chevet inequality and derive the Dvoretzky– Milman theorem, which states that random low-dimensional projections of high-dimensional sets appear nearly round. Exercises cover matrix and process-level deviation bounds, high-dimensional estimation techniques such as the Lasso for sparse regression, the Garnaev–Gluskin theorem on random slicing of the cross-polytope, and general-norm extensions of the Johnson–Lindenstrauss lemma.

This chapter introduces techniques for bounding random processes. We develop Gaussian interpolation to derive powerful comparison inequalities for Gaussian processes, including the Slepian, Sudakov–Fernique, and Gordon inequalities. We use this to get sharp bounds on the operator norm of Gaussian random matrices. We also prove the Sudakov lower bound using covering numbers. We introduce the concept of Gaussian width, which connects probabilistic and geometric perspectives, and apply it to analyze the size of random projections of high-dimensional sets. Exercises cover symmetrization and contraction inequalities for random processes, the Gordon min–max inequality, sharp bounds for Gaussian matrices, the nuclear norm, effective dimension, random projections, and matrix sketching.