# vMAP > Kong 2023 · [Paper](https://arxiv.org/abs/2302.01838) **One-line summary** — Object-level neural-field SLAM in which every detected object gets its own tiny MLP, all trained simultaneously through vectorised operations — watertight, model-free per-object reconstruction at 5 Hz map updates with up to 50 objects per scene. ## Problem Neural-field SLAM systems like iMAP and NICE-SLAM represent the whole scene as one monolithic field with no object-level structure, and extracting individual objects is hard because "the correspondences between network parameters and specific scene regions are complicated". Object-level SLAM, meanwhile, needed CAD models or category-level shape priors to complete unseen surfaces — without priors only the directly observed parts get reconstructed, leaving holes. vMAP targets the no-prior case: efficient, watertight, per-object reconstruction inside a live RGB-D SLAM system. ## Method & architecture **Object initialisation & association.** Each frame carries dense instance masks (ground truth, or Detic pre-trained on LVIS). Detections are associated across frames by two criteria — semantic consistency (same predicted class) and spatial consistency (mean IoU of 3D object bounds); unmatched detections spawn a new object MLP appended to the model stack. Per-object 3D bounds come from the depth-backprojected point cloud and are refined as observations accumulate. Camera poses are provided externally by ORB-SLAM3 — found "more accurate and robust compared to jointly optimising pose and geometry". **Vectorised training** (the key contribution). All object MLPs share one architecture (4 layers, hidden size 32; the background model uses 128), so they can be stacked and optimised as a single batched computation with PyTorch's vectorised operations instead of a Python loop. Each object samples pixels from its own independent keyframe buffer, so any object's training can stop or resume with no inter-object interference. **Depth-guided sampling.** Along each ray, $N_c$ points are stratified-uniform between the near bound $t_n$ and the depth-map surface $t_s$, and $N_s$ points concentrate near the surface: $$t_i \sim \mathcal{U}\Bigl(t_n + \tfrac{i-1}{N_c}(t_s - t_n),\; t_n + \tfrac{i}{N_c}(t_s - t_n)\Bigr), \qquad t_i \sim \mathcal{N}(t_s, d_{\sigma}^{2}),$$ with $d_\sigma = 3$ cm; invalid depth falls back to the far bound. **Occupancy rendering.** View direction is omitted (surfaces over view-dependent appearance) and each point has occupancy probability $o_\theta(\mathbf{x}_i) \in [0,1]$, giving termination probability $T_i = o(\mathbf{x}_i)\prod_{j