Alignment of XIXth century cadasters

Introduction

TODO: Examples of references (APA style).

About a thousand of French napoleonian cadasters have been scanned and need from now to be aligned. A lot of different cities are included in this catalogue as La Rochelle, Bordeaux, Lyon, Lille, Le Havre and also cities that are no longer under French juridiction as Rotterdam.

Similarly to the work that had been done by the Venice Time Machine project, the idea is to attach every maps from a cadaster in order to get a single map of each city.

The main challenge for this project is the automatisation of this process, despite all inconsistencies in the maps, in terms of scale, orientation or conventions. Even if the instructions for the realisation of the maps were quite strict, some differences might last, for example in the scale, if there were nothing to show in some areas, or maps are not always oriented top-north (which is even not always indicated).

Deliverables

- [ ] Tool 
   - [ ] rectification
   - [ ] Alignment
   - [ ] JSON generation
   - [ ] reconstruction of covered areas
- [ ] PoC: La Rochelle downtown

This project provides an exploration of possible automation for aligning cadastres, as well as the development of an interface (in the form of a Jupyter Notebook) to supervise this task.

Project setup

Methods exploration on Berney's cadaster

For the primary research of methods to reattach cadastral maps, the so called cadastre Berney from Lausanne (1827) has been used, as long as the ground truth for this particular case is known and lot of processing steps (as lines and classes predictions) have already been made. The first exercise has been made on the two first maps, using the lines prediction files. The quandary was to be able to detect the common parts of these two maps, in this case the Rue Pépinet and the top of Rue du petit chêne. Many different methods have been tested for that task, mainly with help of the openCV python library. The researches have focused on scale invariant feature transform (SIFT), General Hough Transform (GHT) and Template Matching (TM).

Template matching principle

Template matching is an OpenCV function provided under the name cv.matchTemplate(). It takes as an imput a large scale image and smaller one, called template, that it will try to find in the first image. Concretely, the function slides the template through the initial image and for each position, gives a score of closeness. Note that the template always fully overlap the image, therefore the template must be fully included in the image. The function gives then as an output a matrix with score for each position. It then easy to find the position of the best score.

This function is known to have better results on greyscale images. It is therefore a wise decision to apply it on the lines detected files.

First reattachment of two cadastral maps

The method that gave the most satisfying results (in terms of final output and computation time) was the template matching. The strategy is to cut a template in one of the maps and find the best match in the other one. Attaching the two maps together is then an almost straightforeward task, as long as the lines prediction files are only black (0) or white (255) pixels, and the final result is just the sum of the two of them adapted with the best matching position.

• 

  Berney 001

• 

  Template manually selected from Berney 001

• 

  Berney 002

Heatmap of the Template Matching process and detected template on the target image.

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Alignment of Berney's 1827 cadastral maps 001 and 002

Organisation

Timeline summary of first steps

	Matching method	Template extraction	Growth
Week 4	SIFT	-	1 to 1
Week 5	SIFT and GHT	Manual	1 to 1
Week 6	GHT and TM	Manual	semi-automated 1 to 1
Week 7	GHT and TM	Manual	semi-automated 1 to 1
Week 8	TM	Manual and along lines	semi-automated 1 to 1
Week 9	TM	Manual and along lines	1 to 1 or N
Week 10	TM	Manual and along lines	1 to 1 or N

Final milestones of semester

	Objective
Week 11	Extract lines on a first set of cadastral maps (La Rochelle or Bordeaux) & manage pipeline
Week 12	Test pipeline on the new extracted lines files
Week 13	Adapt our model or extend it on other cities
Week 14	Final presentation

Automatisation process

Automatic extraction of 9 templates. Best match found is satisfying.

Automatic extraction of 8 templates. Best match found is not satisfying.

- [ ] Trials 
   - [ ] Automatic template extraction
   - [ ] Adjacent cadastres considerations: iterative growth
   - [ ] Taking into account: both orientation and scale
- [ ] Low computational Efficiency
- [ ] Necessity to fine-tune manually parameters due to the lack of a metric closer to human understanding
- [ ] Sometimes poor results (eg. less dense areas, etc.)
- [ ] Too fragile method ?
- [ ] And still time consuming and need close supervision => change of paradigm

After this liminary result, a lot of question were nevertheless still to be answered. For example, is the orientation of our maps precisely in the North direction ? Will it be possible to have an explicit order of maps reattachment ? Will the matching score be as good in the countryside as it was in the city ? Is the scale homogenous within an entire city ? Or what criteria could be used to automatise the template selection ?

• Iterative growth with successive anchors 001, 009, 010 and 008. Taking into account slight variations in orientation and two scales.
• 

  Before matching 006 onto 008. Matches are satisfying.

• 

  After matching 006 onto 008. Semantically wrong match.

Due to these limitations, we decided to shift paradigm and to develop a tool more closely supervised.

AlignmentTool

[ ] Jupyter Innotater
[ ] Rectifying
   [  ] rotation
   [  ] name
   [  ] NOT IMPLEMENTED: scale
[ ] Matching process
   [  ] template selection
   [  ] target selection
   [  ] orientation dependent or not
[ ] Output = "raw" network
[ ] Rebuilding
   [  ] homographies
   [  ] pairwise visualisation
   [  ] area growth
      [  ] new network
      [  ] inverse homographies included
      [  ] shortest path

The AlignmentTool was developed to offer a highly supervised method to perform the cadastres' alignment. The backend processes are mainly handled through OpenCv, the data structure is managed with NetworkX, and the Notebook interface relies on jupyter-innotater. The architecture and proceeding of each of these components are detailed below. Finally, the results of the proof of concept undertook on La Rochelle intramural Napoleonic cadastres from 1811 are described and illustrated.

Backbone

Matching

Visualisation of the template's top left and bottom right corners on the anchor cadastre (left, cadastre E) and their corresponding points on the target cadastre (right, cadastre D).

Homography

In the context of this project, homographies are restricted to Euclidean transformations (allowing rotations and translations but preserving the distance between every pair of points). However, as the rest of the implementation is more general, slight modifications of the homographies' computation could enable the intergration of more complex transformations (eg. affine or projective) within the pipeline.

• Alignment of cadastres with direct edge or through propagation.
• 

  Direct match from A1 to D.

• 

  Propagation of matches A1 to A2 to B to C to D.

Network structure

The matches (when selected by the user) are collected in a directed graph. The nodes are the cadastres (or their labels) and the edges link the anchors (cadastres within which templates have been extracted) to their targets (cadastres matched). The edges store information about the matches between anchors and targets: their score and informations related to the matched positions (top left and bottom right corners of the extracted template in the anchor and corresponding positions in the target). An exemple of a possible realisation of such graph (for La Rochelle, 1811) is shown below.

These graph can be saved in JSON format with the following generic structure:

Network visualisation.

{
    "directed": true,
    "multigraph": false,
    "graph": {},
    "nodes": [{
        "h": int — height of the corresponding image,
        "w": int — width of the corresponding image,
        "label": str — name
    }, {
        "h": int — height of the corresponding image,
        "w": int — width of the corresponding image,
        "label": str — name
    }],
    "match": [{
        "score": float — score of the template matching process,
        "anchor_tl": tuple: two int — coordinate of the template top left corner on the anchor,
        "anchor_br": tuple: two int — coordinate of the template bottom right corner on the anchor,
        "target_tl": tuple: two int — coordinate corresponding to anchor_tl on target,
        "target_br": tuple: two int — coordinate corresponding to anchor_br on target,
        "anchor": str — name of the anchor cadastre\node,
        "target": str — name of the target cadastre\node
    }]
}

User guide

Matching flowchart.

Discussion and limitations

- [ ] Lack of convincing metric / purely qualitative results
- [ ] Failing to automate the task

Future Work

- [ ] Tool roadmap
   - [ ] Integration of other matching methods
   - [ ] Integration of more automation (adjacent matching)
   - [ ] improve UX
- [ ] Taking into account matches from all adjacent cadastres and recursive adjustments 
   - [ ] eg. Bundle Adjustment
- [ ] Automation
   - [ ] more heuristic and domain knowledge — in traditional ML/CV methods
   - [ ] investigate "deeper" approaches => add some literature: eg.  
- [ ] Alignment on Openstreetmap