Data Model

GeoTensor

The GeoTensor is the primary citizen of Ununennium. It wraps a PyTorch tensor and ensures that geospatial operations are mathematically consistent.

Affine Representations

The affine transform matrix \(M\) defines the relationship between pixel space \((u, v)\) and projected map space \((x, y)\):

\begin{bmatrix} x \\ y \\ 1 \end{bmatrix} = \begin{bmatrix} a & b & c \\ d & e & f \\ 0 & 0 & 1 \end{bmatrix} \begin{bmatrix} u \\ v \\ 1 \end{bmatrix}

Where: - \(a\): pixel width - \(e\): pixel height (usually negative) - \(c, f\): top-left origin coordinates - \(b, d\): rotation terms (usually 0 for north-up images)

Coordinate Propagation

When performing operations like pooling or strided convolution, the affine transform is updated automatically.

For a stride \(s\):

M_{new} = M_{old} \times \begin{bmatrix} s & 0 & 0 \\ 0 & s & 0 \\ 0 & 0 & 1 \end{bmatrix}

GeoBatch

A GeoBatch is a collection of GeoTensors. It supports stacking tensors even if they are from different non-overlapping regions, tracking their individual metadata for reconstruction.

Bounding Boxes

Bounding boxes are represented as (minx, miny, maxx, maxy) tuples, automatically handled in CRS operations.