### Table 1. Different motion patterns (first column) and the ranks of the generalized structure tensors for 1 and 2 motions respectively (columns 2 and 3). Bars indicate motions of 1D (straight) patterns and filled circles motions of 2D patterns - see text for further details. The shown correspondences between the different motion patterns and the ranks of the two tensors can be used to identify the different motion patterns. In general, the rank of JN, N = 1, 2, ... induces a natural order of complexity for patterns consisting of N additive layers [12].

2004

"... In PAGE 5: ...earing and disappearing objects, etc. correspond to rank J1 = 3. Remarkably, in the case of transparent motions, the categorization of the moving patterns is again accessi- ble through the rank J2. Table1 summarizes these correspondences. For further details see [12].... ..."

### Table 2. Different motion patterns ( rst column) and the ranks of the generalized structure tensors for 1, 2, and 3 motions (table rows). This table summarizes our results by showing the correspondence between the different motion patterns and the tensor ranks that can, in turn, be used to estimate the con dence for a particular pattern, i.e., a proper motion model. Note that the rank of JN induces a natural order of complexity for patterns consisting of N additive layers.

"... In PAGE 5: ... 4.1 Two 1D Transparent Moving Gratings In the projective plane, two moving gratings correspond to the fline, lineg case - see Table2 . According to the theory, the perceived motion should correspond to the intersection point U of the two lines and indeed it does - see Fig.... In PAGE 7: ... In the current framework, the in- trinsic dimension corresponds to the rank of J1. As shown in Table2 , by introducing the generalized structure tensor, we can further differentiate the signal classes of a given (integer) intrinsic dimension. In some sense, we thereby de ne frac- tional intrinsic dimensions.... In PAGE 12: ... These correspond to ranks 1,4 and 2,5,7 respectively. Table2 summarizes the possibilities for the ranks of JN for N = 1; 2; 3. Cicero Mota is on leave from University of Amazonas, Brazil and is currently with the Insti- tute for Neuro- and Bioinformat- ics, University of Luebeck, Ger- many.... ..."

### Table 1: Complexity Comparison of TensorLSI and LSI

"... In PAGE 2: ... When we want to keep the first k principle component in the transformed tensor space, we sort f(ui, vj) for all the i and j in decreasing order and choose the first k pairs. Table1 lists the computational complexity comparison of TensorLSI and LSI, more detailed analysis can be found in [1]. 3.... ..."

### Table A.1: Linearly independent isotropic tensors of ranks up to six

2007

### Table 1: Comparison of our tensor embedding methods with NPE, LPP and LDE in terms of the space complexity and time complexity.

"... In PAGE 6: ...ensors and Imax = max{I1, . . . , Ik}. Table1 compares the space complexity and time complexity of our methods with the previous methods. Since the number of data points n is usually far less than H in many real-world applications, it is clear that our tensor embedding methods are more ap- pealing in terms of both complexity measures.... ..."

### Table 1: Complexity Comparison of TensorLSI and LSI Time complexity Minimum memory Storage size

2006

Cited by 1

### TABLE I. Irreducible spherical components TL quot; quot;) of the tensor Tin terms of the Cartesian components T7,, of the symmetric second-rank tensor.

1990

### Table 1: Nonvanishing components of a symmetric second rank tensor in relation to the tetrahedral vector system

1996

Cited by 1

### Table I: Generic rank r of symmetric tensors as a function of dimension K and order d.

### Table 1. Complexity control scheme ranking error (%)

2003

"... In PAGE 5: ...nly 0.2% absolute worse than the actual best one. A good complexity control scheme should correctly rank all the systems. Table1 shows the recognition performance ranking prediction error computed using the method in section 5.1.... ..."

Cited by 5