User-manual/Image-orthorectification.md

@@ -93,4 +93,22 @@ You can also enter the water level (in m) in this **_Others_** tab. This value w
 
 ![image46](uploads/c6ee056df6239e42072c8452e6ead375/image46.png)
 
-The **_Apply_** button allows you to transform the first image with the entered parameters to get an idea of the result. The **_Validate_** button saves the scaling parameters, displays the first transformed image, and allows you to move on to the next step (Transformation of all images).
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+The **_Apply_** button allows you to transform the first image with the entered parameters to get an idea of the result. The **_Validate_** button saves the scaling parameters, displays the first transformed image, and allows you to move on to the next step (Transformation of all images).
+
+# :triangular_ruler: Full Orthorectification
+
+## Principle of Orthorectification
+
+Orthorectification consists of creating an image corrected for perspective effects and scaled to the real-world dimensions, for a given plane.
+
+<details><summary><b> :mag_right: In-depth explanation :tools: </b></summary>
+<br>
+
+## :mag: The Pinhole Camera Model and its Solution: General 3D Case
+
+We consider a pinhole camera model that allows us to transform an object with coordinates X, Y, Z in a real-world reference frame to its representation i, j in an image reference frame. The relationship between these coordinates can be written in the Direct Linear Transformation (DLT) form as:
+
+```math
+i=\frac{a_1 \cdot X+a_2 \cdot Y+a_3 \cdot Z+a_4}{a_9 \cdot X+a_{10} \cdot Y+a_{11} \cdot Z+1} \quad j=\frac{a_5 \cdot X+a_6 \cdot Y+a_7 \cdot Z+a_8}{a_9 \cdot X+a_{10} \cdot Y+a_{11} \cdot Z+1}
+```
+