When a visual representation retain strong references to real world appearances it is called what type of depiction?

17.3.1 Visual Representation

Visual representation techniques in CAS aim to display all available data to the surgeon in order to facilitate pre and intraoperative decision-making. At the most basic level, visualization techniques are applied to medical images to show the patient’s anatomy, the relevant pathology, and the embedding of the latter in the former. The next step is to add virtual surgical instruments and implants to the visualization, enabling the surgeon to study the interaction between these foreign objects and the existing anatomy and pathology. Finally, simulations of patient function as well as surgical interactions can be visually represented to further assist the decision-making process.

Anatomy and Pathology The primary concern of visual representation of anatomy and pathology is to faithfully and accurately communicate patient anatomy and pathology to the surgeon. CAS systems often rely on volume data, such as CT and MRI, in which case there are three basic visualization techniques that can be applied [Brodlie and Wood, 2001]: multiplanar reformation or slicing, surface rendering and direct volume rendering.

In multiplanar reformatting (MPR), or slicing, data is sampled along an arbitrarily positioned and oriented plane in the data. Oblique angles are possible with this type of visual representation, and they are used in some application areas such as spinal surgery (in which the cutting plane is aligned with the planned access path). However, surgeons, especially in orthopedics, are more attuned to the standard axial, sagittal, and coronal views which they were taught, possibly with an additional 3D view [Lattanzi et al., 2002].

Curved Planar Reformation, or CPR, is a variation on this theme where data is sampled along a curved planar structure, usually determined by some anatomical structure, such as blood vessels. CPR is discussed in detail in Chapter 11. An example using CPR for maxillofacial surgery planning is discussed in § 17.5.1.

Surface rendering, discussed in Chapter 6, entails extracting surfaces, often represented as polygons, from the volume data, either by isosurfacing, or converting segmented objects to surfaces, and then displaying the extracted surfaces. In CAS literature, this is still used far more frequently than direct volume rendering. This is largely due to the fact that surface rendering has a longer history in medical applications, and that medical users have built up quite some experience with its use and interpretation.

With direct volume rendering, or DVR, volumetric data is displayed without an intermediate surface extraction step, instead either casting light rays through the data or projecting volume data points onto the display. DVR is discussed in detail in Chapters 7 and 8Chapter 7Chapter 8. In contrast to surface rendering, DVR is able to display more volumetric information at the same time, and offers great flexibility in specifying the appearance of the resulting renderings. In CAS solutions however, this flexibility is often seen as a disadvantage. Furthermore, surfaces still offer more possibilities in terms of structural simulation, and in the representation of anatomy and surgical instruments in motion.

Besides the three standard types of visual representation techniques, there are examples of techniques built for a specific purpose, such as the visual representation of vessels, see Chapter 11. This is used for example in hepatic surgery, see § 17.5.4. In an interesting example of intraoperative visualization, Hansen et al. [2010a] projected illustrative representations of liver anatomy and the embedded lesions onto the liver during surgery, in an augmented reality setup. Figure 17.2 shows an example of this.

Virtual Surgical Actions To be able to plan surgery, it should be possible to perform the procedure, or parts of it, virtually. This is also called process simulation and is discussed in detail in § 17.3.3, while the actual interaction techniques are briefly discussed in § 17.3.2.

The results of these virtual surgical actions need to be visually represented using a suitable metaphor. When a joint prosthesis or screw is virtually placed for example, this should be shown in such a way that the user can judge whether risk structures have been avoided and sufficient bone contact has been attained.

Predicted Outcome An overview of the different types of simulation techniques that are used in CAS will be given in § 17.3.3. Especially simulation techniques that try to predict the outcome of a procedure or action generate data that can also be used to enrich existing visualizations. Enhancing visualizations in this way can help operating surgeons to fine-tune their decision-making.

For example, Krekel et al. [2006] show the interactively calculated postoperative shoulder range of motion with motion envelopes that represent the maximum reach of the shoulder joint. In addition, the difference between two surgical options in terms of postoperative range of motion is explicitly visualized as green (improvement) and red (deterioration) polygons (Fig. 17.6).

Another example is that of Dick et al. [2009], shown in Figure 17.3, who interactively calculate stress in bones before and after an endoprosthesis is virtually placed.

1.1 Visual Representation

Studies of visual representation in science include analyses of published and unpublished images, and of the historical crafts and technologies responsible for their production. Currently, there are numerous disciplinary and cross-disciplinary approaches to visual representation. Representation is simultaneously a philosophical, historical, and cultural concept. Social, cultural, and literary studies of science include a bewildering array of historicist, semiotic, feminist, cognitivist, epistemological, pragmatist and other lines of interpretation. All of these appear, often in combination, in studies of visual representations. As many cultural and literary studies have emphasized, visual representations do not simply resemble natural objects: they express normative assumptions about natural and cultural worlds; they incorporate historically and culturally specific artistic conventions; and they mediate political and cultural relations of patronage, commodity exchange, and subjugation (Newman 1996, Haraway 1997).

c Diagram Representation of W-Operators.

A visual representation of operators is useful to illustrate some concepts. Here the diagram representation of binary W-operators used henceforth is introduced. Given W, binary signals in {0, 1}W can be represented as subsets of W or, equivalently, as elements in {0, 1}d. Suppose that W = {w1, w2, w3}, the binary signal g ∈ {0, 1}W with g(w1) = 0, g(w2) = 0, and g(w3) = 0 corresponds to the element 000 ∈ {0,1}3, and so on.

The set {0, 1}d with the usual ≤ relation (i.e., for any u = (u1, u2,…, ud), v = (v1, v2,…, vd) ∈ {0,1}d, u ≤ v if and only if ui ≤ vi, i = 1, 2,…, d) is a partially ordered set. Together with the usual logical operations (OR +, AND ·, and NEGATION ·¯), it forms a Boolean lattice. Partially ordered sets can be depicted by Hasse diagrams. The diagram at the left side of Figure 2 corresponds to the representation of {0, 1}3. Each element of the lattice is represented by a vertex and two vertices corresponding to elements u and v, such that u < v, are linked if and only if there is no other element w such that u < w < v. The diagram at the right side corresponds to the representation of the function ψ: {0, 1}3 → {0, 1} with ψ(111) = ψ(011) = ψ(101) = ψ(001) = 1 and ψ(110) = ψ(010) = ψ(100) = ψ(000) = 0. Elements in {0, 1}3 mapped to 1 are depicted by solid circles, whereas those mapped to 0 are depicted by open circles. In particular, in this example ψ is increasing (i.e., if ψ(u) = 1, then ψ(v) = 1 for any v > u). If a W-operator is increasing, whenever an element is solid, all elements above it (according to the partial order relation) are necessarily solid in its Hasse diagram representation.

2.3.3 Interpolation Artifacts

Many visual representations use interpolation schemes to compute data at positions between defined grid points. A popular scheme is trilinear interpolation (Eq. 2.3) for position and normal computation.The normals in volume datasets are usually approximated by gradients using central differences Höhne and Bernstein [1986]. Assuming a uniform grid with the distance h between voxels in x -, y- and z-direction central differences, compute the gradient at p(xi,y i,zi) as the difference between adjacent voxels in all 3D according to Equation 2.4

(2.4)∇f(x i,yj,zk)=xi+1-xi-12h,yj+1-yj-12h,zk+1-zk-12hT

Unfortunately, central differences will cause artifacts, if the intensity differences are large, or the grid spacing is anisotropic.

In the case of binary segmentation, individual voxels are labeled as part of the segment (on) or not part of the segment (off). If the respective isosurface representing the material interface between the segment and its neighborhood is computed, large intensity differences on the material interface (all off-voxels are set to zero, all on-voxels contain the original voxel value) occur. In these situations, the positions of the isosurface and in particular their normals will experience the above-mentioned artifacts and result in a blocky appearance (Fig. 2.9).

Fortunately, there are several remedies for these interpolation artifacts, if the original data is used for isosurface computation and the label volume is only used as a map to indicate the voxels of the segments. The first remedy adds a layer of off-voxels around the segment voxels. This additional off-layer allows smoother local gradients on the material interface of the segment, since the intensity differences are significantly smaller than to zero intensities, due to the partial volume effect [Höhne and Bernstein, 1986]. Another possible remedy changes the original data values. Here, the material interface in the voxel values is processed by a low-pass volume filter, which generates a smooth transition between the segment and the off-voxels. However, this also changes the resulting isosurface and must hence be applied with great care.

A related interpolation issue arises also with the normal estimation based on central differences on anisotropic grids. Typically, the normal at a computed sample point within a volume cell is based on the trilinear interpolation of normals approximated by central differences at the surrounding voxels of this volume cell. This gradient estimation scheme, however, assumes an isotropic grid, since all three vector components are computed the same way. Since anisotropic datasets have different voxel distances in the three different spatial orientations, these differences are not properly addressed in most rendering approaches. The normals at the computed sample points are distorted in the different spacing direction. There are several solutions that reduce staircasing artifacts [Möller et al., 1997]. More recently, Neumann et al. [2000] suggested to use linear regression to estimate better gradients.

VIII Decay Scheme Representations

For concise visual representation, the decay path (or paths) of every radionuclide is usually shown by a decay-scheme graph. The decay scheme shows energy, in millions of electron volts, above the ground state of the product nuclide (taken as zero) as the ordinate and atomic number in integral units as the abscissa. A β− decay is shown as a diagonal arrow terminating one unit in Z to the right of the Z of the radionuclide. A decay by EC or β+ emission is shown as a diagonal arrow terminating one unit in Z to the left of the Z of the radionuclide. Decay by α emission is shown by a diagonal arrow terminating two units in Z to the left of the Z of the radionuclide. Gamma-ray transitions are shown by vertical arrows going from an excited state of the product nucleus to the ground state, or to a lower excited state. In branched decays, the percentage of transitions following a given decay path is shown. Some decay schemes (i.e., those decaying purely by α, β−, or β+ emission, or by EC or IT by a single γ transition) are very simple. Others are more complicated, and some are very complicated. Usually included in each decay scheme is the Q value (Qβ−, QEC, Qα, etc.) for the transition of the radionuclide to the ground state of the product nuclide via that mode of decay.

2.1.2 Site Map

This is a visual representation of the contents of the site by section and subsection shown as a hierarchy that usually reflects the site's navigation. You will no doubt have used site maps extensively during the project planning and definition stages, so it should just be a matter of updating your site map to reflect the current extent of the site.

If you are fortunate, you will have a software tool that can automate this for you. Many content management systems, or simpler site management tools such as various automated File Transfer Protocol (FTP) publishing tools, include a feature allowing you to create a site map.

The power net

To get a visual representation of your political situation you can draw yourself and your relationships and the power that flows between you in both directions.

Draw a circle in the center of a page to represent yourself.

Draw circles to represent specific people with whom you interact. Draw these circles closer to you for people with whom you spend a lot of time and further away for those who have an important effect on your work though they may not spend much time interacting with you (patients, suppliers, commissioners, for example).

Draw lines to connect yourself with all of the people. On the lines write what type of power each person in your net has in relation to you. Do they have the right to decide what you do? What information do you need? What is the basis of their power? What sort of power do you have in relation to them?

You can also think of the power net in terms of dependence: who depends on you for what? And who do you depend on for what?

1.1.1.1 Images

An image is a visual representation of something that depicts or records visual perception. For example, a picture is similar in appearance to some subject, which provides a depiction of a physical object or a person. Images may be captured by either optical devices, such as cameras, mirrors, lenses, and telescopes, or natural objects and phenomena, such as human eyes or water surfaces. For example, in a film camera works the lens focuses an image onto the film surface. The color film has three layers of emulsion, each layer being sensitive to a different color, and the (slide) film records on each tiny spot of the film to reproduce the same color as the image projected onto it, the same as the lens saw. This is an analog image, the same as our eyes can see, so we can hold the developed film up and look at it.

Images may be two-dimensional, such as a photograph, or three-dimensional, such as a statue or a hologram. An image in a broad sense also refers to any two-dimensional figure such as a map, a graph, a pie chart, or an abstract painting. In this sense, images can also be rendered manually, such as by drawing, painting, carving; can be rendered automatically by printing or computer graphics technology; or can be developed by a combination of methods, especially in a pseudophotograph. In photography, visual media, and the computer industries, the phrase “still image” refers to a single static image that is distinguished from a kinetic or moving image (often called video), which emphasizes that one is not talking about movies. The phrase “still image” is often used in very precise or pedantic technical writing such as an image compression standard.

In this book, we consider two-dimensional still images in a broad sense. Thus, an analog image (physical image) I defined in the “real world” is considered to be a function of two real variables as follows:

(1.1)I={I(x,y)∈[0,B]|0≤x≤X ,0≤y≤Y}

where I(x,y) is the amplitude (e.g., brightness or intensity) of the image at the real coordinate position (x,y), B is the possible maximum amplitude, and X and Y define the maximum coordinates. An image may be considered to contain subimages sometimes referred to as regions. This concept reflects the fact that images frequently contain collections of objects, each of which can be the basis for a region.

Analysis using charts

Charting information allows for visual representations that can help interpret data, and turn a complex investigation into an easy to understand concept. The type of chart depends upon the type of information to be displayed. Link charts and matrix charts show relationships, flow charts and event charts show a sequence of events or processes, and organization charts show hierarchy.

The matrix chart has been discussed in a previous chapter as a means of identifying and eliminating potential suspects. Although simple, the matrix chart is extremely effective given almost any number of potential suspects and can quickly be understood. See Figure 5.1 as an example of a matrix chart.

Link charting is another method to quickly visualize relationships between persons or events. As a data analysis method, suspected or confirmed relationships are immediately made obvious through symbols. A basic foundation of symbols used in a link chart can be seen in Figure 6.14. Through the use of basic and simple symbols, clarity in relationships becomes obvious.

Using the basic design symbols from Figure 6.14, an example has been created in Figure 6.15. In this example, it is clearly seen that only Suspect B has access to both evidence computers, PC 1 and PC 2. Suspect C has access only to one evidence computer and Suspect A might have access to PC 1.

Suggestions for link charts include avoiding crossing lines to avoid confusion, and keep the charts simple and to as few points as possible. Solid connecting lines are confirmed relationships whereas dotted lines are not confirmed. If there is not a relationship between a person and/or evidence item, then no connecting line is made, showing no relationship. Although Figure 6.15 is a simple example, it only takes seconds to see relationships without requiring explanation even if the data was more intensive.

The creation of link charts can be made using paper and pens or using any number of software applications. Microsoft Visio (http://www.microsoft.com) is one example of a program developed for this type of diagram. As seen in Figure 6.16, Visio allows for easy creation of link charts and analysis with pre-defined shapes and symbols. Programs developed specifically for data analysis, such as the IBM i2 Analyst’s Notebook (http://www.i2group.com), allow for automated creation of links, charts, and graphs. These more powerful programs have advanced features of data analysis beyond creating link analysis diagrams which may be necessary in large investigations.

Event and flow charts can be used to display a chronological chain of events of an investigation or a computer application process. Figure 6.17 shows the requirements to physically access a computer which was used to send an email under investigation. The chart implies only one employee had physical and login access rights to the suspect computer out of over 100 persons at the location. Actual cases will most likely require more complex charting but the concept remains the same; visually show facts to more easily see the less obvious.

Used in combination to the information displayed in Figure 6.16, a visual timeline created from both a forensic analysis of the suspect computer and investigative information can be seen in Figure 6.18. By employing several analytical methods to analyze information, a narrowing list of suspects is created or may show that only one suspect could have committed the alleged acts.

2.2 Modeling

A superstructure-based optimization approach is employed to simultaneously synthesize and design a chemical process coupled with the power generation, water treatment and CCU sub-networks.

2.2.2 Generic interval model

The generic interval model gives the general form of the mathematical model for each interval to support the mathematical representation of the total network. As illustrated in Figure 2, the generic interval model has 5 operating units to convert the inlet flows to the outlet flows: a mixer, a reactor, a carbon emission calculation unit, a waste separator, and a product separation unit.

Figure 2. Generic interval model for multi-network stochastic programming.