...up

Throughout this paper, I treat verb-particle constructions, like pick up, as atomic verbs, despite the fact that the verb and its associated particle may be discontinuous. Methods for deriving the semantics of a verb-particle construction compositionally from its (discontinuous) constituents are beyond the scope of this paper.

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...overlapped,

I am using the term `overlap' here in a different sense than the 43#43 relation from [4]. Here, I am using the term overlap in the sense that two intervals overlap if they have a nonempty intersection. This corresponds to the union of the 43#43, 44#44, 45#45, 46#46, 47#47, 48#48, 49#49, and 50#50 relations from [4].

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...interval.

To deal with noise, in the actual implementation, the primitive event type 52#52 is derived from the predicate 51#51 by first passing 51#51 through a low-pass filter that takes 53#53 to be the majority vote of a five-frame window centered on t.

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...to z.

Originally, a two-interval definition was used, consisting of only the first and third intervals. Such a definition better reflects human intuition. This requires that x be unsupported, y not support either x or z, x and z not support each other, and y not be attached to z throughout the event. Unfortunately, however, the model-reconstruction process has some quirks. When the hand grasps the patient while the patient is still resting on the source it produces a most-preferred model where all three objects are attached and collectively supported by one of them being grounded. While such a model is consistent with the theory and is minimal, it does not match human intuition. Pending improvements in the model-reconstruction process to better reflect human intuition, the compound event-type definition for pick up was modified to reflect the force-dynamic interpretations produced by the current model-reconstruction process. Fortunately, the current model-reconstruction process is robust in reproducing this counterintuitive interpretation.

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...respectively.

Throughout this paper, I use lowercase Greek letters, such as 150#150, 151#151, 152#152, 153#153, 154#154, and 155#155, to denote Boolean values, lowercase Latin letters, such as p, q, r, i, j, k, and l, to denote real numbers, lowercase bold Latin letters, such as 41#41, 69#69, and 107#107, to denote intervals or spanning intervals, and uppercase Latin letters, such as I, J, and K, to denote sets of intervals or sets of spanning intervals.

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...interval.

The reason that 240#240 contains at most one normalized spanning interval and not exactly one normalized spanning interval is that 41#41 may denote the empty set of intervals. For example, normalizing the (non-normalized) spanning interval [[10,10],[1,1]] yields the empty set. Many of the definitions in the coming sections compute sets of normalized spanning intervals as unions of one or more applications of the normalization operator 242#242. Each such application might yield either the empty set or a set containing a single normalized spanning interval. This leads to upper, but not lower, bounds on the size of the computed unions.

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...sequences.

The code for LEONARD, the video input sequences discussed in this paper, and the full frame-by-frame output of LEONARD on those sequences is available as Online Appendix 1, as well as from ftp://ftp.nj.nec.com/pub/qobi/leonard.tar.Z.

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...size=-1>EONARD.

The movies, as well as the results produced by LEONARD when processing the movies, are available as Online Appendix 1, as well as from ftp://ftp.nj.nec.com/pub/qobi/leonard.tar.Z.

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