"... In PAGE 5: ... Results for each speaker are shown on separate plots. Table4 shows the classification results on the low-resolution test data for Speaker 1. The first column shows the size of the Gaussian kernel used to blur the original high- resolution images.... ..."

"... In PAGE 6: ... The main task lies in splitting and re- triangulating the triangles belonging to both the low-res and high-res mesh in the overlapping regions (see the top right diagram of Figure 11). Possible intersections of a low-res triangle and the con- vex hull are summarized in Table1 . There are three pos- Figure 9: Possible intersections between a low-resolution triangle and the convex hull of high-resolution mesh.... ..."

"... In PAGE 1: ... The one-step inferences in this case are shown in Table 3. We also consider the even coarser situation in which there are only two possibilities of interest: #5Cdisjoint quot; and #5Coverlap quot; #28 Table4 #29. Overlap in this case is just the negation of disjoint #28it means the two objects have... In PAGE 4: ... Then relational consistency according to Tables 1-4 will reveal no contradiction. For instance, in the simplest case of Table4 any topological relation between a pair of objects is permitted regardless of the relations between the other pairs of objects. However, there is no way to realize this set of relations by a set of regions in the plane, without having two of the Y objects overlap.... In PAGE 4: ... Constraint satisfac- tion problems are typically NP-complete, although spe- cial classes can be solved in polynomial time. In the constraint satisfaction problems arising in con- nection to topological inference, the variables are pairs of distinct objects; all domains are the subsets of the set of eight topological relations in Table 1 #28or the #0CveinTa- bles 2 and 3, or the twoin Table4 #29, as dictated by the clause corresponding to the pair of objects; and for each triple #28i; j; k#29 of objects wehave a constraint, namely, that the value of the pair i; j, the value of the pair j; k, and the value of the pair i; k must be related as in Table 1 #28or 2, or 3, or 4#29. For example, the topological expression #28A overlaps B _ A equal B#29 ^ #28B contains C#29 ^ #28A inside D _ A contains D#29 is expressed by six variables #28all unordered pairs of ob- jects from A, B, C, D#29.... In PAGE 5: ... Entries 5, 13, 21. Since Table4 imposes no real constraintinlow resolution, all topological expressions are satis#0Cable. Incidentally,ifwe allow general Boolean combinations of relational statements instead of topo- logical relations #28that is, clauses that involve statements about more than one pair of objects#29, then this entry be- comes NP-hard: We can simulate Boolean satis#0Cability byhaving an object for eachvariable, and also another object 0, and replacing all instances of variable x with #5C0 disjoint x quot; and the negation of x with #5C0 overlap x quot;.... ..."