Semiotica 131 (2000), 1-18.
A fundamental problem in the practice of diagnostic radiology is to draw inferences about conditions at an anatomic boundary by observation of its radiographic image. This is a type of inverse projection problem (Epstein 1995) where information about a source (distal event) is inferred from information in a target (proximal event). In diagnostic radiology the simplest form of this inverse projection problem involves the detection of the presence or absence of disease. In clinical practice, a solution of the detection problem is commonly expressed in terms of a radiological sign, where the presence of a sign implies the presence of disease. We note that the problem of detecting the absence of disease is more complex due to the phenomenon of disease latency and that the mere absence of a sign may not imply the absence of disease.
In this study, diagnostic radiographic signs will be called Roentgen signs. Signs that may be seen in an arbitrarily small neighborhood of an image point will be called local signs. In what follows, we develop a general typology for local Roentgen signs based on the structural semiotics of Roman Jakobson and the semeiotic of Charles S. Peirce.
A radiographic boundary is the interface between contiguous regions of a radiograph that are distinguished by visual contrast. Since radiography is basically a central projection (Dance 1993), a necessary condition for the formation of a radiographic boundary is tangential incidence of the x-ray beam with the corresponding anatomic boundary. This condition produces spatial separation in the image. Since radiography is also a type of transmission imaging (Dance 1993), another necessary condition for the formation of a radiographic boundary is the presence of a sufficient difference of attenuation of the x-ray beam on the two sides of the corresponding anatomic boundary to produce visual contrast in the image. In what follows, we will say that this condition produces contrast separation in the image. Together, these two necessary conditions are sufficient for the radiographic image of an anatomic boundary to form a radiographic boundary. Since an anatomic boundary separates two contiguous regions of space, the corresponding radiographic boundary separates two contiguous regions in the image. Hence, visual separation is the combined perceptual effect of both spatial separation and contrast separation.
When a visual boundary is perceived, spatial dichotomies such as inside-outside or figure-ground are evoked in the mind of the viewer (Atmanspacher and Dalenoort 1994:1-12). In other words, a radiographic boundary separates contiguous regions in the image that correspond to the inside and outside of an anatomic boundary. The global topological property of spatial separation (cf. The Jordan Separation Theorem) has as counterpart a local property that holds in an arbitrarily small neighborhood of a boundary point. There are two distinct types of local visual separation that occur at radiographic boundaries. In what follows, these are called line-separation and edge-separation.
Line-separation occurs when the boundary between two complementary regions of an image is a line that is distinguished from the two regions by visual contrast. In other words, a boundary line separates the inner (figure) from the outer (ground) components of the complement of the line in an arbitrarily small neighborhood of a boundary point (Figure 1). This will be called the line-separation effect. In radiology, the line- separation effect is created by the interlobar fissures of the lungs, the articular cortexes of joints, and other anatomic interfaces.
Edge-separation occurs when an enclosed region of an image and its contiguous complement are distinguished by visual contrast. In other words, an edge boundary of an enclosed region separates inside (figure) from outside (ground) in an arbitrarily small neighborhood of a boundary point (Figure 2). This will be called the edge-separation effect. In radiology, the edge-separation effect is created by the cardiopulmonary interface, the mucosal surface of gas filled bowel, and other anatomic interfaces.
In what follows, the general process by which the conceptual dichotomy inside-outside is evoked by perception of a radiographic boundary will be called the visual separation effect. This term will refer to either line-separation or edge-separation.
In diagnostic radiology, some pathologic processes that occur near an anatomic boundary may result in an absence of the visual separation effect that is normally seen in an image of that boundary. In other cases, a pathologic process that occurs near an anatomic boundary may result in the presence of a visual separation effect that is not normally seen in an image of that boundary. We propose that absence of an expected visual separation effect be called a loss of separation sign and that the presence of an unexpected visual separation effect be called a gain of separation sign. Furthermore, the presence of one type of visual separation where another type is expected will be called an exchange of separation sign.
To summarize: since a naturally occurring radiographic boundary may present as a line or an edge, there are two basic types of visual separation effect, one involving line-separation and the other edge-separation. Consequently, there are two distinct loss of separation signs, one based on the absence of expected line-separation and the other based on the absence of expected edge-separation. Similarly, there are two distinct gain of separation signs, one based on the presence of unexpected line-separation and the other on the presence of unexpected edge-separation.
In order to describe specific radiographic signs, we must first define the concept of visual contrast as used in diagnostic radiology. In clinical practice, visual contrast is a perceived difference in optical density between adjacent regions of an image. The term optical density refers to a level on a gray scale. By gray scale we mean a distribution of shades of gray that varies continuously from black to white. In diagnostic radiology, the materials commonly encountered in the human body have characteristic optical densities. Specifically, the optical density of air is black, fat a shade of gray, water equivalent tissues (i.e. tissues with high water content such as muscle) a lighter shade of gray than that of fat, and the optical density of bone is white. Consequently, there is a natural radiographic contrast between air, fat, water equivalent tissues, and bone. Note that in this sequence, optical density varies directly with physical density. Hence, optical densities may be graded on the basis of their relative brightness. By convention, relatively light optical densities are called radiopacities and relatively dark optical densities are called radiolucencies. Therefore, normal radiographic boundaries may present as radiopaque or radiolucent lines or edges. We are now in a position to classify the separation signs that occur at radiographic boundaries.
The loss of separation signs
These signs are produced at anatomic boundaries that normally present as lines or edges. At a radiopaque line the sign is due to a local loss of contrast separation between the line and both components of its relatively radiolucent complement. In this case line-separation is lost. This sign may be formed in two ways.
At a radiopaque edge, the loss of separation sign is due to a local loss of contrast separation between the enclosed region and its relatively radiolucent complement. In this case edge-separation is lost. This sign may be formed in two ways.
Clearly, the loss of separation sign may be defined, in a dual fashion, at radiographic boundaries that present as a radiolucent line or edge. At a radiolucent line the loss of separation sign is formed by a local increase in radiopacity of the line to the same level as its relatively radiopaque complement. Radiolucent boundary lines within relatively radiopaque soft tissues are produced by tangential images of layers of peribursal, intermuscular, or intra/extraperitoneal fat. In these cases, the opacity of fat is increased to that of the adjacent soft tissues by soft tissue edema (Resnick 1995:2954, 4593) or ascites (Messmer 1994:188). Similarly, the radiolucent edge at the interface between subcutaneous fat and skeletal muscle may be obscured by edema (Resnick 1995:4593).
The gain of separation signs
These signs occur in the interior of anatomic compartments and are due to the creation of abnormal interfaces i.e. new interior boundaries. In such cases, the gain of separation sign involves the formation of an unexpected radiopaque or radiolucent line as in fracture of bone or an unexpected radiopaque or radiolucent edge as with circumscribed soft tissue masses.
The exchange of separation signs
These signs are produced at anatomic boundaries that normally present as lines or edges. These signs may be formed in two ways.
In what follows we will be concerned with the gradient or rate of change of optical density across radiographic boundaries. When this gradient is sufficiently steep (rapid) a boundary is said to be sharp and when it is sufficiently gradual (slow) the boundary is said to be unsharp. Therefore, unsharpness means decreased sharpness. It is well known (Curry et al. 1990:206-207) that unsharpness of a radiographic boundary may result from factors such as the imaging system employed (geometric and film-screen unsharpness), movement of the object edge (motion unsharpness), and the shape of the object edge (absorption unsharpness). To these factors the clinical radiologist may add the effects of disease (disease unsharpness). With all other factors held constant, the sharpness of a radiographic boundary may either increase or decrease as a consequence of disease at the corresponding anatomic boundary. In other words, a difference between the observed and the expected sharpness of a radiographic boundary may be a sign of disease.
We propose that the absence of an expected boundary gradient (or the presence of an unexpected gradient) in a tangential image of an anatomic boundary be called a gradient sign. Since gradients may be expressed numerically and are linearly ordered, there can be only two gradient signs which we will define in terms of sharpness. The loss of sharpness sign appears when an observed gradient is less than expected (i.e. the normal). The gain of sharpness sign appears when an observed gradient is greater than expected (i.e. the normal). Clearly, these signs are local boundary signs.
In the author's experience, the gradient signs have been decisive for the early detection of some abnormalities. The loss of sharpness sign appears in skeletal radiology where unsharpness of the articular cortex (endplate) of vertebral bodies is an early sign of uremic osteopathy (Cantor and Kattan 1993:Figure 8) and unsharpness at bone/soft tissue interfaces is an early sign of hyperparathyroidism (Resnick 1995:1903). In chest radiology, unsharpness of a cardiopulmonary or phrenopulmonary interface is an early sign of pneumonia or atelectasis (Fraser and Paré 1988:618). The gain of sharpness sign appears in skeletal radiology at vertebral endplates due to osteoporosis (Resnick 1995:1813). In chest radiology, unexpected sharpness of a cardiopulmonary or phrenopulmonary interface is a subtle sign of pneumothorax (Fraser and Paré 1988:683).
Up to this point, we have studied two types of local boundary signs: the separation and gradient signs. We will now discuss density signs which are a type of local interior sign. Such signs appear in an arbitrarily small neighborhood of a point on the inside of a radiographic boundary line or edge. Since optical density is perceived only in a neighborhood of a point (the concept of optical density does not apply to a dimensionless point), signs based solely upon the perception of optical density must be local signs.
The field of diagnostic radiology is based upon the recognition that some diseases may alter the x-ray attenuating properties of human tissues. Consequently, such diseases will produce optical density changes on radiographs. On this basis, the absence of an expected optical density (or the presence of an unexpected optical density) inside a radiographic boundary will be called a density sign. Since the gray scale of optical densities is linear, there can be only two density signs. These may be defined in terms of opacity. The loss of opacity sign appears when the observed optical density is less than expected (i.e. normal). The gain of opacity sign appears when the observed optical density is greater than expected (i.e. normal).
In clinical practice, the density signs are most commonly used for the detection of disease. The loss of opacity sign is used in skeletal radiology to detect osteolysis (Resnick 1995) and it is used in chest radiology to detect pneumothorax (Fraser and Paré 1988:683). The gain of opacity sign is used in skeletal radiology to detect osteosclerosis (see the analytic index in Resnick 1995) and it is used in chest radiology to detect pneumonia and atelectasis (Fraser and Paré 1988:467).
The Separation Signs
The reader may verify that the loss of separation signs and gain of separation signs are related by a duality (cf. Duality Principle). This means that the signs transform into one another when the pairs of terms absence/expected and presence/unexpected are interchanged in their definitions. This duality gives rise to three symmetric pairs of binary relations between visual separation effects. Each of these binary relations is asymmetric (i.e. a binary opposition) and represents a separation sign. Let us recall that a separation sign is a relation between unexpected (abnormal) and expected (normal) visual separation effects. If A is a separation effect that is unexpected and B is the separation effect that is expected, then the corresponding separation sign may be represented symbolically as A→B. If we also indicate the absence of a separation effect by ASE, the presence of a line-separation effect by LSE, and the presence of an edge-separation effect by ESE, then all of the separation signs are represented in Figure 10. Specifically, the loss of line-separation sign is denoted by ASE→LSE, the gain of line-separation sign by LSE→ASE, the loss of edge-separation sign by ASE→ESE, and the gain of edge-separation sign by ESE→ASE. Note that the bottom edge of the triangular diagram in Figure 10 is comprised of the exchange of separation signs for which the observation of one type of separation is in opposition to the expectation of the other type.
The gradient signs
Recall that a gradient sign is a relation between an unexpected (abnormal) and the expected (normal) degree of sharpness of a boundary line or edge. In fact, the loss of sharpness and gain of sharpness signs form an antisymmetric pair of binary relations between observed and expected boundary gradients. Let B represent the expected degree of sharpness of a boundary. If the observed degree of sharpness is less than B, it may be represented by Am, where the subscript m stands for minus. If the observed degree of sharpness is greater than B, it may be represented by Ap, where the p stands for plus. In this way, the gradient signs may be represented symbolically as Am→B (the loss of sharpness sign) and Ap→B (the gain of sharpness sign).
The density signs
Recall that a density sign is a relation between an unexpected (abnormal) and the expected (normal) optical density in the interior of an image. In fact, the loss of opacity and gain of opacity signs form an antisymmetric pair of binary relations between observed and expected optical densities inside of a boundary. The same notation may be used for the density signs as was used for the sharpness signs. Let B represent the expected interior opacity, Am the observed opacity when it is less than B, and Ap the observed opacity when it is greater than B. Then the density signs may be represented by Am→B (the loss of opacity sign) and Ap→B (the gain of opacity sign).
The concept of markedness (cf. Waugh 1982, Andrews 1990) describes the types of asymmetry that may occur in binary relations. In general, a binary relation is an ordered pair of terms. In an asymmetric binary relation one term is said to be marked and the other unmarked. The marked term indicates the presence or statement of a property. Roman Jakobson (1957:136) distinguished two types of unmarked terms that correspond to the two types of asymmetric binary relations (binary oppositions) that occur in phonology and grammar. In one type, the unmarked term indicates that the property is absent. In this case, called the general type, the absence of a property is placed in opposition to its presence. In the other type, called the specific type, the negation of a statement is placed in opposition to the statement itself. Any binary opposition between a marked term A and an unmarked term B may be represented symbolically as A→B. By convention, the arrow points away from the marked term and toward the unmarked term.
The concept of markedness may be adapted to Roentgen semiotics in a natural way. A Roentgen sign has been defined as a binary opposition of visual percepts where the observed (the abnormal) is in opposition to the expected (the normal). In this way, the observed corresponds to the marked term and the normal is unmarked. Furthermore, it is implicit in our discussion of binary oppositions that the separation signs are of the general type while the gradient and density signs are of the specific type. Therefore, the two types of Roentgen signs, as determined by the type of the unmarked term, may be represented as A→Bg and A→Bs where A is the marked term, Bg is unmarked in the general sense, and Bs is unmarked in the specific sense. All of the Roentgen signs discussed up to this point have been detectors of disease i.e. signs of the abnormal. Each sign is an asymmetric binary relation between observed and expected visual percepts. We will now define a Roentgen sign that is a symmetric binary relation between observed and expected visual percepts. In this sign, the observed is what is expected (i.e. the normal). This sign of the normal is in opposition to all signs of the abnormal and therefore is a zero sign (Jakobson 1939). This zero sign may be represented symbolically as A→A where the arrow is directed away from the observed and toward the expected (i.e. the normal).
In the perception of a normal radiographic image, boundaries are identified by the presence of a visual separation effect (PSE) and interior regions are identified by the absence of a visual separation effect (ASE). The pair of terms PSE and ASE form an oppositive duality such that "if one of the terms is given, then the other, although not present, is evoked in thought" in the same way that black evokes white and vice versa (Jakobson 1976:235). Neither PSE nor ASE can be expressed in terms of simpler visual percepts. In this sense they are irreducible (indivisible or minimal). Therefore, PSE and ASE form a binary opposition of irreducible visual features. Since PSE and ASE serve to distinguish between two types of image points i.e. boundary and nonboundary points, they function as discriminating features. In other words, PSE and ASE represent irreducible differences in visual experience that distinguish between boundary and nonboundary points. In this way, PSE and ASE may be regarded as distinctive features in Roentgen semiotics since they function in the same way as distinctive features in phonology (cf. Jakobson 1952, 1976). More specifically, since radiographic boundaries may present as either line-separation or edge-separation effects, both clearly in opposition to the absence of separation effect, these two visual percepts are distinctive features in Roentgen semiotics.
There is another principle of phonology that may be adapted to Roentgen semiotics. To paraphrase Jakobson et al. (1952:252): '[If] perceptually there exists a continuous range of degrees [of a phonic quality], only two polar points are picked out as distinctive features.' Applying this principle to boundary gradients, the terms relatively sharp and relatively unsharp are distinctive features in binary opposition. The same principle may be applied to the quality of optical density that appears on either side of a boundary (inside or outside). In this case, the terms relatively radiopaque and relatively radiolucent are distinctive features in binary opposition.
While there is a functional similarity between phonological and visual distinctive features (they are both minimal discriminators), they differ in their semantic content. Jakobson emphasized that phonological distinctive features have no meaning in themselves. However, the visual distinctive features encountered in Roentgen semiotics have contextual meaning. The presence or absence of a line or edge on a radiograph has specific meaning within a context that is extrinsic to the image. We have seen that the presence of a radiographic boundary in an image may represent a normal boundary or an abnormal interior (the gain of separation sign) while the absence of a radiographic boundary may represent an abnormal boundary (the loss of separation sign) or a normal interior.
In the perception of a radiographic boundary line or edge, the distinctive features of separation and gradient coexist and are inseparable. Therefore, any boundary percept consists of at least a pair of distinctive features: separation and gradient. Such a pair (bundle) of visual distinctive features may be called a viseme in analogy with the phoneme which is a bundle of phonic distinctive features (Jakobson et al. 1952). Transposing the words of Roman Jakobson et al. from the context of structural phonology to that of Roentgen semiology, it is not unreasonable to suggest that '... on the visual level, image analysis may be conducted in terms of binary visemic oppositions' (cf. Jakobson et al. 1952:254).
Charles S. Peirce conceived of a sign as a triadic relation (cf. Liszka : chapter 2) between a representamen (signifier), an object (signified) and an interpretant (meaning to someone). The question will be asked: what is the relation between Roentgen signs, as we have defined them, and Peircean signs? If S is a Peircean sign with signifier V, object O and interpretant I, then it may be represented symbolically as S:VO. In what follows, it will be useful to define a specific sign in which the signifier and signified are the same and the interpretant is a relation of identity that is independent of time. This is a zero sign (cf. Jakobson 1939) and it will be represented as Z:A→A where A is any term and the arrow without a modifier is understood to be the identity interpretant. According to Peirce, any sign may be reinterpreted to form a new sign. A priori, there is no limit to the number of new signs that may be created in this way. This process of unlimited reinterpretation is represented diagrammatically in Figure 11 where I1, I2 and I3 are three successive interpretants. Note that in this scheme the signifier V and signified O never change. Only the interpretant changes with the creation of a new sign. Furthermore, the top and bottom edges of the diagram are made up of zero signs. In fact, the zero sign was defined in order to make this diagram commutative. By this, we mean that a given sign VO may be reinterpreted to obtain a new sign VO where VO→O is the same sign as VO and V→VO is the same sign as VO, etc.
In clinical practice, a Roentgen sign is a binary opposition between the observed and the expected. In this context, the term expected means previously observed and presently remembered (cf. the role of expectation in speech cognition, Jakobson : 240). In other words, a Roentgen sign is a relation between a percept and a memory of a percept and a radiographic sign may be thought of as an interpretant of a Peircean sign. For example, consider the Roentgen separation signs i.e. the loss of separation, gain of separation and exchange of separation signs. Let V represent a neighborhood on a film containing a part of a radiographic boundary and let O represent a neighborhood of a part of an anatomic boundary, the tangential image of which is the given radiographic boundary. If I1 is the interpretation of V as a faithful representation of O (i.e. one that preserves the relation inside/outside), then S1:VO is a Peircean sign. Note that the interpretant I1 is based upon an understanding of the radiographic process i.e. its geometry and physics. If I2 is the interpretation of V that O is normal, then S2:VO is a Peircean sign. In this case, the interpretant I2 is based upon the personal experience of the observer and the experience of others that has been communicated to the observer. Finally, if I3 is the interpretation of V that O is abnormal, then S3:VO is a Peircean sign where the interpretant I3 is based upon the absence of an expected visual separation effect. Therefore, this interpretant is what we have previously regarded as a radiographic sign of disease.
We have classified local radiographic signs of disease at boundaries on the basis of visual separation effects. We have shown that for both line-separation and edge-separation there is a loss of separation sign, a gain of separation sign, and an exchange of separation sign. It must be emphasized that the separation signs will be perceived only by a prepared mind. The prepared observer must have a thorough knowledge of normal radiographic anatomy and anatomic variation. Only then may the observer anticipate whether a given separation effect occurs or does not occur under normal conditions.
On a more fundamental level, we have found a basis for the general study of Roentgen signs in the principles of structural semiotics as developed by Roman Jakobson and in the semeiotic of Charles S. Peirce.
The computer graphics were executed by Jan Warren, M.A.