## Why "Intogral"?

Where does the name Intogral Limited come from?

The most high-level problems of image segmentation, computer graphics, and finite element analysis can be expressed with simple definitions using integrals.

For example, the Mumford-Shah functional establishes an optimality criterion for segmenting an image into sub-regions:

$$E[u,C] = \int_{\Omega} (u - I)^2 dx + \mu \int_C \left|\nabla u \right|^2 dx + \nu \left|C\right|$$

Or the rendering equation, which describes how to model light to give photorealistic rendered images:

$$L_o(\mathbf{x},\omega_o,\lambda,t)=L_e(\mathbf{x},\omega_o,\lambda,t)+\int_\Omega f_r(\mathbf{x},\omega_i,\omega_o,\lambda,t)L_i(\mathbf{x},\omega_i,\lambda,t)(\omega_i \cdot \mathbf{n}) \mathrm{d}\omega_i$$

While there are many differnt ways to solve these equations, using them as a base allows us to produce a "mathematically-correct" solution within the constraints and parameters.

At intogral limited, we are committed to doing things properly. We produce exact solutions to challenging problems such as segmentation and structural analysis. That is "inside" an "integral": intogral.