Sequence space

In functional analysis and related areas of mathematics, a sequence space is a vector space whose elements are infinite sequences of real or complex numbers. Equivalently, it is a function space whose elements are functions from the natural numbers to the field K of real or complex numbers. The set of all such functions is naturally identified with the set of all possible infinite sequences with elements in K, and can be turned into a vector space under the operations of pointwise addition of functions and pointwise scalar multiplication. All sequence spaces are linear subspaces of this space. Sequence spaces are typically equipped with a norm, or at least the structure of a topological vector space. The most important sequence spaces in analysis are the ℓ''p'' spaces, consisting of the p-power summable sequences, with the p-norm. These are special cases of Lp spaces for the counting measure on the set of natural numbers. Other important classes of sequences like con

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Tracking Multiple Objects under Global Appearance Constraints

Horesh Beny Ben Shitrit, Jérôme Berclaz, François Fleuret, Pascal Fua

In this paper, we show that tracking multiple people whose paths may intersect can be formulated as a convex global optimization problem. Our proposed framework is designed to exploit image appearance clues to prevent identity switches. Our method is effective even when such clues are only available at distant time intervals. This is unlike many current approaches that depend on appearance being exploitable from frame to frame. We validate our approach on three multi-camera sport and pedestrian datasets that contain long and complex sequences and demonstrate better performance than state-of-the-art algorithms.

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2011

Tracking Multiple People under Global Appearance Constraints

Horesh Beny Ben Shitrit, Jérôme Berclaz, François Fleuret, Pascal Fua

In this paper, we show that tracking multiple people whose paths may intersect can be formulated as a convex global optimization problem. Our proposed framework is designed to exploit image appearance cues to prevent identity switches. Our method is effective even when such cues are only available at distant time intervals. This is unlike many current approaches that depend on appearance being exploitable from frame to frame. We validate our approach on three multi-camera sport and pedestrian datasets that contain long and complex sequences. Our algorithm perseveres identities better than state-of-the-art algorithms while keeping similar MOTA scores.

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2011

Multi-Commodity Network Flow for Tracking Multiple People

Horesh Beny Ben Shitrit, Jérôme Berclaz, François Fleuret, Pascal Fua

In this paper, we show that tracking multiple people whose paths may intersect can be formulated as a multi-commodity network flow problem. Our proposed framework is designed to exploit image appearance cues to prevent identity switches. Our method is effective even when such cues are only available at distant time intervals. This is unlike many current approaches that depend on appearance being exploitable from frame to frame. Furthermore, our algorithm lends itself to a real-time implementation. We validate our approach on three publicly available datasets; APIDIS basketball dataset, ISSIA soccer dataset and the PETS’09 pedestrian dataset, all contain long and complex sequences. In addition, we evaluate the approach on a new basketball dataset, consists of full world championship basketball matches. In all cases, our approach preserves identity better then the state-of-the-art tracking algorithms.

Institute of Electrical and Electronics Engineers2014

Banach space

In mathematics, more specifically in functional analysis, a Banach space (pronounced ˈbanax) is a complete normed vector space. Thus, a Banach space is a vector space with a metric that allows the co

Hilbert space

In mathematics, Hilbert spaces (named after David Hilbert) allow the methods of linear algebra and calculus to be generalized from (finite-dimensional) Euclidean vector spaces to spaces that may be

Locally convex topological vector space

In functional analysis and related areas of mathematics, locally convex topological vector spaces (LCTVS) or locally convex spaces are examples of topological vector spaces (TVS) that generalize norm

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