Mobile Document Scanner

Implement a mobile document scanning application that converts photos of documents into clean, readable scans. This task involves image processing and computer vision techniques to detect document boundaries, correct perspective distortion, and enhance the document for readability. The process can be mathematically represented as a series of transformations, including $x' = \frac{x}{z}$ and $y' = \frac{y}{z}$ for perspective correction, where $(x, y, z)$ are the coordinates in 3D space and $(x', y')$ are the coordinates in the 2D image plane.

1. Detect document boundaries in the photo using edge detection techniques, which involve calculating the gradient of the image intensity function $I(x, y)$.
2. Correct perspective distortion using perspective transforms, which can be represented by a $3 \times 3$ matrix $\begin{pmatrix} a & b & c \\ d & e & f \\ g & h & i \end{pmatrix}$.
3. Enhance the document for readability using image enhancement techniques, such as adaptive thresholding, which can be mathematically represented as $T(x, y) = \frac{1}{W^2} \sum_{(x', y') \in W} I(x', y')$, where $W$ is a window of size $W^2$.

This technique is widely used in document scanning and processing applications.