Reading 3D Structure from 2D Edges

One intensity step, several possible causes

A catalog of edges in the blocks world

Nonaccidental properties and the generic view

From edge orientation to linear constraints

In the blocks world, a thresholded edge map shows a nearly horizontal image edge, and the vertical scanline through it enters colored object pixels above the edge and white ground pixels below it. The edge sits where a block rests on the ground. What is this edge, and what does it contribute to the reconstruction?

Two straight image lines meet exactly at a junction. Which conclusion about the 3D scene does the cotermination argument support, and what makes the competing explanation unlikely?

A camera views the blocks world with tilt angle $\theta$ satisfying $\cos(\theta) = 3/5$. The system detects a 3D vertical edge, and the constraint on the world height map along this edge is $\frac{\partial Y}{\partial y} = \frac{1}{\cos(\theta)}$. Write the value that the finite-difference constraint $Y(x, y) - Y(x, y-1)$ takes along the edge.