### Table 1: The morphological axioms.

"... In PAGE 3: ... We are now in the position to define the Morpho-logic. The morpho-logic is a theory in the hybrid arrow logic whose ax- ioms are shown in Table1 . We present it as an extension of the arrow logic of Definition 2.... In PAGE 3: ...6 (Notation) As a point of notation, we use KHAL for the axiomatization of the hybrid arrow-logic. Of all the axioms presented in Table1 , the axiom (rev31) and (rev32) are the most notable ones. The purpose of the axioms is to give the relations C, R and I a group semantics.... In PAGE 3: ... Proof. First, we note that the axioms in Table1 are pure formulas. Then, we remark that every pure formula is di- persistent.... In PAGE 6: ... QED 4 Concluding Remarks Driven by the Mathematical Morphology view of space, we introduced a language based on hybrid arrow logic to reason about space. The logic, which is a theory in the hybrid arrow logic defined by the axioms of Table1 , is a powerful lan- guage to express morphological as well as mereotopological properties of space. To reason in the morpho-language we introduced a resolution calculus.... ..."

### Table 1: The morphological axioms.

2006

"... In PAGE 4: ...he world labeled i, i.e., a world that satisfies i. We are now in the position to define the Morpho-logic. The morpho-logic is a theory in the hybrid arrow logic whose ax- ioms are shown in Table1 . We present it as an extension of... In PAGE 5: ... We do not report here the full axiomatization of the hybrid arrow language as it can be found in [de Freitas et al., 2002], but rather report the new axioms with morphological significance ( Table1 ). As a point of notation, we use KHAL for the ax- iomatization of the hybrid arrow-logic.... In PAGE 5: ... As a point of notation, we use KHAL for the ax- iomatization of the hybrid arrow-logic. Of all the axioms presented in Table1 , the axiom (rev4) is the most notable one. The purpose of the axioms is to give the relations C, R and I a group semantics.... In PAGE 5: ... Proof. First, we note that the axioms in Table1 are Sahlqvist formulas. Second, the relations C are R versatile, in the sense of [Venema, 1993].... In PAGE 7: ... QED 4 Concluding Remarks Driven by the Mathematical Morphology view of space, we introduced a language based on hybrid arrow logic to reason about space. The logic, which is a theory in the hybrid arrow logic defined by the axioms of Table1 , is a powerful lan- guage to express morphological as well as mereotopological properties of space.... ..."

### Table 14. Overlapping between cameras and size of skin locus in the colour space.

2002

"... In PAGE 71: ... It can be concluded from these tables, that the overlap between different skin groups was in all cases reasonably high. Table14 compares the overlap between different cameras and the percentage occupied by the constraint from the total area. As shown in this table, the total overlap between all cameras is much lower than the overlap between brightness (gain) controlled cameras (Alaris and Nogatech) and be- tween cameras without it (Sony and Winnov).... ..."

### Table 3. Analysis of morphological errors

2004

"... In PAGE 5: ...ormalizations, i.e. 36.9% of the tokens were normalized. Table3 presents a breakdown of the errors encountered. The miscellaneous category indicates places where unusual tokens such as non-breaking spaces were replaced with actual words, an artifact of tokenization in the NLPWin system.... ..."

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### Table 1: Characteristics of special morphologies.

1999

"... In PAGE 4: ... Mohr et al. (1957) first used the striation thickness (see Table1 ), defined as one-half the spacing between layer midplanes in a lamellar structure, as a measure of mixing. Striation thickness is related to the specific area of a lamellar mixture by = 1 SV (2.... In PAGE 5: ....2.2 Example Area Tensors When the mixture has one discrete and one continuous phase, the area tensor provides information about the shape and size of the discrete-phase domains. Table1 shows the area tensors for three example mixture morphologies. The area tensor is triaxial (isotropic) for spherical domains, biaxial (transversely isotropic) for cylindrical domains, and uniaxial for lamellar structures.... In PAGE 5: ... We can then define a local characteristic length scale Lc for the discrete phase as the ratio of the total volume Vd of the discrete phase within V to the total interfacial area Sd within V Lc Vd=Sd = =SV (2.8) Table1 gives the characteristic length scales for the three example morphologies. The characteris- tic radius of the lamellar structure is related to the striation thickness by r = .... In PAGE 14: ... This approximation is generated by choosing a functional form, constraining the form, and fitting the constrained function to data generated from the exact closure. The constraints force the closure to obey geometric symmetries, give exact results in the three limiting cases of Table1 , and have correct asymptotic behavior near those limits (Wetzel and Tucker, 1997). Exact data for ^ A (1), ^ A (2), and ^ A (3) as a function of ^ A(1) and ^ A(2) were generated using Eqns.... In PAGE 22: ... (2.8) and Table1 with a dispersed-phase volume fraction = 0:10, this tensor represents a lamellar morphology with an average sheet... ..."

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### TABLE I Obtained results with the mathematical morphology method detection. Breast type Light tissue Dense tissue Light tissue Dense tissue

in Automated Detection And Separation Of Microcalcifications By Multi-Scale Analysis Of The T. H. T.

### Table 2 shows the five categories into which sources may be categorised. The MI values are presented both for CIELAB and CIELUV colour difference calculations, as the average length of colour difference vectors in the two colour spaces differ.

"... In PAGE 7: ... Table2 : Categories of sources based on metamterism indices. In stating the quality of a daylight simulator by this method, first the category designator for the visible range metamerism index has to be given, followed by the ultraviolet range category descriptor, and the colour space used in brackets.... ..."

### Table 1: Comparison of 8 Colour Spaces Note: the first row is the number of images that have the greatest evaluation values in different colour spaces, the second line and the third row are the sum and average of the evaluation values in different colour spaces respectively.

2000

"... In PAGE 6: ... The statistical result is summarised in Table 1. From Table1 we can see that among the 120 testing images, 117 images have the greatest evaluation value in the rg space than in others. So according to our evaluation function, we selected rg space to perform skin area detection tasks.... ..."

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### Table 1: Parameters associated with morphological operation.

"... In PAGE 7: ... It comprises two, two-stage morphological operators and a linear classifier. The parameter space for each morphological operation is summarized in Table1 . All functions exploit reconstruction [10].... In PAGE 7: ... We evolved populations of 25 chromosomes, for 25 generations. The probabilities for mutation (for each parameter in Table1 ), and uniform crossover (which randomly swaps complete operations), were both 0.15.... ..."

### Table 2. Below: space of ML applications to word morphology. Above: preference biases used to augment training data annotation.

2000

"... In PAGE 10: ... We want to suggest a classi cation of all possible applications of ILP learning to word morphology based on two factors, the extent to which linguistic concepts are used as background concepts, and the amount of annotation in data. The lower part of Table2 (see page 18) gives a graphical representation of that clas- si cation. The horizontal axis represents a partial ordering between data sets|if two data sets containing the same words are displayed in di erent columns, the one on the left-hand side contains all annotation from the rst data set plus some additional one.... In PAGE 11: ...available in the data. The application of any preference bias for unsupervised learning from the upper part of Table2 would result in a right-to-left move in parallel to the horizontal axis. Indeed, each of these biases would add extra annotation to the data yet their contribution to the concept language would usually be limited to the creation of new theory constants, typically segments of words.... ..."

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