Meta-model of cadastral map

4.3 Meta-model of cadastral map

Here after, we present the fruit of many discussions, collaborations and meetings with our partners from Humanities And Social Sciences. Especially, the architect Michel Denès¹ was the investigator of a dictionary which explains how the maps were elaborated and the meaning of many symbols inside the maps. To identify the elements described in the atlas, it is obviously the vocabulary of this historical pe-riod that has been favored. This dedicated vocabulary is inspired from various texts of this period contemporary of the city drawn by Philibert Vasserot. P. Vasserot was the chief geometer in charge of the elaboration of the cadastral map (topological record). The Cécile Souchon’s article published in 2005 lights up several points; the author points out that the maps indicate the divisions between the ground, stairs, courts, gardens, water wells, and ovens. Moreover, the Souchon’s article deals with the paper layout called "Grand Aigle" (105x75cm) and the scale was changed by the geometer if the concerned quarter was too large to fit the paper sheet. Commonly, the documents are recorded using a range of scales from 1/200 to 1/500. Lastly, the article expresses that parcel boundaries walls are stippled with black ink. Now, from the raster image itself, M. Denès made some remarkable observations. Are drawn by instruments: the property limits, walls and gardens. The thickness is set once and for all: frontage walls and dividing walls have the same thickness. Finally, most of painted details are hand-drawn: stairs, common ovens, latrines, etc. From this work, a taxonomy of the cadastral map has arisen providing a natural and textual description of objects that can be found in the rasters. To take note of this knowl-edge, we created a meta-model of cadastral map that can be handled by computer algorithms. The meta-model is displayed in figure4.5under the Unified Model Lan-guage (UML) formalism. This latter denotes inter-relationship of different elements inside the system. The data semantics of cardinality, categorization, N-ary relation-ship are represented and from this complete expression, we focus our attention on a subpart which deals with frame, street, quarter, parcel and text elements. This restraint meta-model is shown in figure 4.6. Simply, this diagram expresses the basic content of the map and how items are laid out: Cadastral map has a frame which encircles the street names, they are materialized as text components. These connected components surround each quarter and text cannot be localized inside a quarter. Finally, a quarter contains many parcels, there is no defined cardinality for that.

4.3.1 Concept definitions

Before explaining our methodology, we want to visualize what a parcel is for an historian. In figure4.7, a parcel was manually vectorized by an expert. This parcel

1The École nationale supérieure d’architecture de Versailles is a French architectural school located at the ancient stables of the Versailles Palace. The school was founded in 1969 after the suppression of the École des beaux-arts architecture section. Architect Jean Castex was one of the school’s founders, while Nicolas Michelin (founder of the group Labfac) is its current managing director.

Figure 4.5: Expert-designed meta-model of cadastral map

4.3. Meta-model of cadastral map 61

Figure 4.6: Limited cadastral map meta-model. Logic of description.

specification leads to the description of the bricks constituting a parcel.

Definition 2. Parcel properties:

• is inside a quarter

• is outlined by thick lines

• two adjacent parcels cannot have the same color

From fine to coarse, figure4.8brings to view examples of a map with two quar-ters. In fact, an image can hold from one to four quarquar-ters. With the time and when working with the maps for a quite long time, clear conclusions can be drawn about quarters:

Definition 3. Quarter properties:

• is surrounded by streets

• is text-less.

By extension, a group of quarters has some basic properties:

Definition 4. A set of quarters:

• is surrounded by streets

(a) Source image (b) Parcel polygonized by an historian

Figure 4.7: Parcel: a visual specification

• is centered in the middle of the map

• is apart from others items (rulers, compass rose...) Here, the notations used to model our problem are defined.

Definition 5. (Frame, Quarter, Street, Character, Parcel) Is defined as Frame, Quarter, Street, Character, Parcel any objects identified by the Frame, Quarter, Street, Character, Parcel detectors, respectively.

4.3.2 Relation definitions

Definition 6. (isOutside) An object isOutside another object if they do not share any features. obj1 and obj2 have no common points. This fact can be represented by the following statement:

|obj1∩obj2|=∅ and,

|obj1∪obj2|=|obj1|+|obj2|

This relation is symmetric and a binary relation is symmetric if it holds for all a and b that if a is related to b then b is related to a.

Definition 7. (contain) This relationship expresses the fact that an object is a composition of others objects. An object overlaps another. We define that an obj1 contains obj2 if they verify the following relation:

|obj1∩obj2|=|obj2|

and,

|obj1∪obj2|=|obj1|

This relation is transitive, a logic relation between three elements such that if it holds between the first and second and it also holds between the second and third it must necessarily hold between the first and third.

4.3. Meta-model of cadastral map 63

(a) Source image

(b) Quarter polygonized by an historian

Figure 4.8: Quarter: a visual specification

Definition 8. (connected) When two white areas are only separated by a black pixel border of one pixel width.

Definition 9. (encircle) When an object surrounds another without intersection.

obj1 encircles obj2 if they verify the following relation:

|BoundingBox(obj1∪obj2)|=|obj1|

and,

obj1∩obj2 =∅

This relation is transitive ans is applied to the elements related to obj1.

Finally, the cardinality of the relations between concepts was analyzed as follows:

Many To Many:

• A case study: Courses are taught by one or many teachers. One teacher can teach on one or many courses.

• In our case : Characters are outside one or many Quarters. One Quarter can have one or many Characters outside.

One To Many:

• A case study: A course has one or many students.

• In our case : A Frame encircles one or many Quarters.

Many To One:

• A case study: Many students belong to one department.

• In our case : Many Parcels belong to one Quarter.

One To One:

• A case study: Office numbers are associated with a unique address.

• In our case : One cadastral map has a unique Frame.

From this model, a list of objects to be retrieved has been enumerated. In the next section, we present the image processing tools especially designed to locate and isolate the characters, the streets, the frame, the quarters and the parcels.