Problem Definition

A General Problem

Suppose an object detection dataset \(S\) contains \(K\) different kinds of objects; each image contains \(M_i\) objects \(o_1, \ldots, o_{M_i}\):

\[S = \{ \mathbf{z}_i \}_{i=1}^n = \{ I_i, \mathbf{y}_{o_1}, \ldots, \mathbf{y}_{o_{M_i}} \}_{i=1}^n\]

where

\[I_i \in \mathbb{W} \times \mathbb{H}\ \times \mathbb{C}\]

\[\mathbf{y}_{o_j} = \{ c_{o_j}, x_{o_j}, y_{o_j}, w_{o_j}, h_{o_j} \} \in \mathbb{K} \times \mathbb{Z}^4\]

where \(c\) denotes object category, \(x\) and \(y\) are the bounding box center coordinates, \(w\) and \(h\) represent width and height of the bounding box respectively [1].

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[1]

\(\mathbb{W} \subseteq \mathbb{Z},\) \(\mathbb{H} \subseteq \mathbb{Z},\) \(\mathbb{C} = \{ 1, 2, 3 \},\) \(\mathbb{K} = \{1, \ldots, K\}\).

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