====== ICA – Independent Components Analysis ======
{{ :intermediate_level:hoku_intermediate_ica.png?nolink&600| }}

**What it does.**

ICA reads a multiband image, computes an Independent Components Analysis transform from a user‑selected ROI, then applies that transform to the full input image. Use ICA when you want to separate statistically independent sources (e.g., underwriting vs. overtext/substrate) that may be mixed across bands.

**When to use ICA vs. PCA/MNF (at a glance).**  
  * **PCA** orders components by **variance**; higher‑order bands may reveal low‑contrast text (see PCA page). [[basic_level:pca_principal_components_analysis|PCA — Principal Components Analysis]]  
  * **MNF** whitens noise first, then outputs bands that often decrease in image quality with band index (see MNF page). [[intermediate_level:mnf_minimum_noise_fraction|MNF — Minimum Noise Fraction]]  
  * **ICA** aims to **unmix independent sources**, often isolating distinct writings/materials better than PCA/MNF in some cases.

===== Inputs =====
  * **input** — multiband image (**Byte**, **Integer**, or **Float**).
  * **roi** — a windowed **Region of Interest** (ROI) from the *same* multiband image; used to **compute** the ICA transform.
  * The **number of bands** on *input* **must match** the number of bands on *roi*. Image sizes may differ.

{{:intermediate_level:ica:roi_dialog.png?400|ROI dialog (example)}}

*Hoku reads the image twice internally: first the ROI to estimate the transform, then the full image as **input** to receive the final transform.*

<WRAP tip center 65%>
**Choosing an ROI for ICA**  
* Pick an ROI that actually contains the features you hope to separate (e.g., underwriting + overtext).  
* Larger ROIs and more bands can make the transform more stable, but will **increase compute time**.  
* If separation looks unstable, try a slightly different ROI (position/size) and/or a different **nonlinearity** (below).
</WRAP>

===== Parameters =====

^ Parameter ^ Meaning ^ Default / Notes ^
| **nonlinearity** | Contrast function used by ICA. Options: **logcosh** (default), **kurtosis**, **gaussian**. | Start with **logcosh**; try others if separation is poor. |
| **iterations** | Maximum iteration count for transform estimation. | **200** |
| **tolerance** | Early stop when change in transform falls below threshold. | **1e‑8** |
| **bandsOut** | Number of output bands to create. | By default equals number of input bands; you may request fewer. |

{{:intermediate_level:ica:ica_arguments.png?480|ICA argument dialog (example)}}

===== Output =====
  * **output image** (Float).  
  * Bands are ordered by **decreasing 2‑D spatial coherence** (average correlation of each pixel with its neighbors to the right and below).  
  * If you specify fewer output bands (e.g., *M*), Hoku outputs bands **0..M‑1**.

{{:intermediate_level:ica:ica_components_grid.png?600|Example: ICA components grid}}

> **Interpreting bands.**  
> Lower‑index ICA bands tend to emphasize spatially coherent structure (e.g., text strokes); higher‑index bands often show finer texture or noise.

===== How it works (very briefly) =====
ICA estimates a linear unmixing transform that produces statistically **independent**, typically **non‑Gaussian** components. The transform is computed from the **ROI** using the chosen contrast function (nonlinearity) and iterative updates until the **tolerance** is met or **iterations** is exceeded. Hoku then applies the final transform to the full **input** image.

===== Performance considerations =====
  * More **bands** and/or larger **ROIs** → longer computation.  
  * If convergence is slow or results look unstable, try a different **nonlinearity** and/or adjust the ROI.

===== Data types =====
  * **input:** Byte, Integer, or Float  
  * **output:** Float

===== See also =====
  * [[basic_level:pca_principal_components_analysis|PCA — Principal Components Analysis]]  
  * [[intermediate_level:mnf_minimum_noise_fraction|MNF — Minimum Noise Fraction]]  
  * [[introduction:hoku_levels|Hoku Levels (ICA is an Intermediate tool)]]