ration.

**AND nodes:** Each part template is an AND node, which uses its children (latent patterns) to represent its constituent or contextual regions. We use $v$ and $Child(v)=\{u_{1},u_{2},\ldots,u_{m}\}$ to denote the part template and its children latent patterns. We learn the average displacement from $\Lambda_{u}$ to $\Lambda_{v}$ among different image, denoted by $\Delta{\bf p}_{u}$, as a parameter of the AOG. Given parsing results of children latent patterns, we use the image region of each child node $\Lambda_{u}$ to infer the region for the parent $v$ based on its spatial relationships. Just like a deformable part model, the parsing of $v$ can be given as $$S_{v}\!=\!\!\!\!\!\!\!\sum_{u\in Child(v)}\!\!\!\!\!\!\!\big[S_{u}\!+\!S^{\textrm{inf}}(\Lambda_{u}|\Lambda_{v})\big],\;\;\Lambda_{v}\!=\!f(\Lambda_{u_{1}},\ldots,\Lambda_{u_{m}})\!$$ where we use parsing results of children nodes to infer the parent part template $v$. $S^{\textrm{inf}}(\Lambda_{u}|\Lambda_{v})$ denotes the spatial compatibility between $\Lambda_{u}$ and $\Lambda_{v}$ *w.r.t.* their average displacement $\Delta{\bf p}_{u}$. Please see the appendix for details of $S^{\textrm{inf}}(\Lambda_{u}|\Lambda_{v})$.

For the region parsing of the part template $v$, we need to estimate two terms, *i.e.* the center position ${\bf p}_{v}$ and the scale $scale_{v}$ of $\Lambda_{v}$. We learn a fixed scale for each part template, which will be introduced in Section \[sec:learnAOG\]. In this way, we can simply implement region parsing by computing the region position that maximizes the inference score ${\bf p}_{v}=f(\Lambda_{u_{1}},\Lambda_{u_{2}},\ldots,\Lambda_{u_{m}})={\arg\!\max}_{{\bf p}_{v}}S_{v}$.

**Terminal nodes (neural units):** Each terminal node under a latent pattern represents a deformation candidate of the latent pattern. The terminal node has a fixed image region, *i.e.* we propagate the neural unit’s receptive field back to the image plane as its image region. We compute a neural unit’s inference score based on both its neura