# 7. astec_postcorrection¶

## 7.1. Post-correction overview¶

The Astec segmentation procedure yields a series of segmented images $$\{S^{\star}_t\}_t$$, where each segmented image $$S^{\star}_{t+1}$$ takes advantage of the knowledge of the previously segmented image $$S^{\star}_t$$ to decide, at the cell level, whether a cell division may occur. However, there are still segmentation errors, that can be detected from the study of the overall lineage (see [Gui15] (section 2.3.3.7, page 74) and [GFL+20] (supp. mat.)).

As suggested by its name, the post-correction will try to a posteriori correct the segmentation resulting from the astec_astec stage (see section astec_astec).

The post-correction is made of the following steps.

1. Lineage pruning: it goes through the end branches (a branch does not have any cell division; an end branch finishes either at the end of the sequence or the cell vanishes between two time points) of the lineage tree. Some lineage end branches are deleted (see section Step 1: lineage pruning for details), meaning that the corresponding cells are fused with other cells of the embryo.

2. Division postponing: some divisions are postponed.

## 7.2. Post-correction / input data¶

Input data are the result of the astec_astec stage (see section astec_astec) and will be searched in the directory SEG/SEG_<EXP_SEG>/ (see section Astec / output data).

/path/to/experiment/
├── ...
├── SEG/
│  └── SEG_<EXP_SEG>/
│     ├── <EN>_seg_lineage.xml.
│     ├── <EN>_seg_t<begin>.inr
│     ├── <EN>_seg_t<:math:\ldots>.inr.
│     ├── <EN>_seg_t<end>.mha.
│     ├── LOGS/
│     └── ...
...


## 7.3. Post-correction / output data¶

The results are stored in sub-directories POST/POST_<EXP_POST> under the /path/to/experiment/ directory where where <EXP_POST> is the value of the variable EXP_POST (its default value is 'RELEASE').

/path/to/experiment/
├── ...
├── POST/
│  └── POST_<EXP_POST>/
│     ├── <EN>_post_lineage.xml.
│     ├── <EN>_post_t<begin>.inr
│     ├── <EN>_post_t<:math:\ldots>.inr.
│     ├── <EN>_post_t<end>.mha.
│     ├── LOGS/
│     └── ...
...


The image format to be used (here mha) is given by the variable result_image_suffix, while the lineage format to be used (here xml) is given by the variable result_lineage_suffix.

## 7.4. Step 1: lineage pruning¶

Bifurcations of the lineage tree correspond to cell division, while branches (between two bifurcations or between a bifurcation and a leaf) corresponds to the lifespan of a cell. The purpose of this step is to detect suspicious end branches (terminating by a leaf) that may correspond to an over-segmentation error.

An end branch is candidate for deletion if

• either it terminates before the last time point (it corresponds then to a cell without daughter cell in the next time point),

• or the volume of its last cell is too small (threshold given by the variable postcorrection_volume_minimal_value).

An end branch candidate for deletion is deleted if

• either it is too short (threshold given by the variable postcorrection_lifespan_minimal_value),

• or (if the variable postcorrection_test_early_division is set to True) either its sister branch (which may not be an end branch) or its mother branch is too short, meaning that there are two divisions too close, (thresholds still given by the variable postcorrection_lifespan_minimal_value),

• or if the Pearson correlation coefficient between the volumes of the candidate end branch and its sister branch is less than -postcorrection_correlation_threshold, meaning that the volumes are anti-correlated (typically the volumes of the candidate end branch are decreasing while the ones of the sister branch are increasing, indicating a fake division detection).

## 7.5. Step 2: division postponing¶

• postcorrection_volume_minimal_value branch ending with leaf cell below this value are candidate for deletion. Expressed in voxel unit.

• postcorrection_lifespan_minimal_value

• postcorrection_test_early_division

• postcorrection_test_volume_correlation

• postcorrection_correlation_threshold

• postcorrection_lineage_diagnosis performs a kind of diagnosis on the lineage before and after the post-correction.