  Real-world objects and environments are predominantly composed of edge
features, including straight lines and curves. Such edges are crucial elements
for various applications, such as CAD modeling, surface meshing, lane mapping,
etc. However, existing traditional methods only prioritize lines over curves
for simplicity in geometric modeling. To this end, we introduce EMAP, a new
method for learning 3D edge representations with a focus on both lines and
curves. Our method implicitly encodes 3D edge distance and direction in
Unsigned Distance Functions (UDF) from multi-view edge maps. On top of this
neural representation, we propose an edge extraction algorithm that robustly
abstracts parametric 3D edges from the inferred edge points and their
directions. Comprehensive evaluations demonstrate that our method achieves
better 3D edge reconstruction on multiple challenging datasets. We further show
that our learned UDF field enhances neural surface reconstruction by capturing
more details.
