Police investigations "à la carte"

University of Liège geomaticians have applied a numerical crime mapping methodology to the simulation of a police investigation. A simulation based on real events, in other words a series of crimes orchestrated by a single gang using a single car. On the basis of information divulged by the Federal Police Force, they had to imagine the most plausible scenario concerning the gang’s itinerary and thus designate on a map the zones which could potentially accommodate their withdrawal site. And the results are astonishing.

Directed by Professor Jean-Paul Donnay, the ULg’s Geomatics Unit from time to time works with the police. One of its most recent research studies sprang from the dissertation by a student, Kenneth Broxham, and was subsequently picked up by two doctoral students. At the outset it was the police who commissioned this study to in order to test the department’s analytical capacities. And the study ended up going beyond our borders to appear in an American reference work (1). ‘The results of the dissertation were presented during a conference on crime mapping, at Washington D.C.,’ explains Jean-Paul Kasprzyk, the publication’s first author. ‘At the end of this presentation, the American Michael Leitner (NB: an internationally recognised researcher in the discipline) suggested we write an article on it.’  

This working together is not surprising. If the USA, together with England and Canada, is the main cradle of crime mapping, the present publication offers an innovative methodology transposable to other enquiries, and more widely to all the disciplines requiring the study of cartographic data.

A case of operational crime mapping

The case in question is thus the simulation of an operational investigation. The police divulged to the University department information about a series of acts committed by a band of criminals.

The information provided was the following: the same group of criminals committed 5 crimes near to Charleroi initiated by the theft of a car, and which took place between May 30 and June 3, 2005. The chronology, the nature and the locations of these acts were known. The time when the car was rediscovered was also established. A final piece of information, and not the most insignificant, the distance travelled by the car between the theft and its being abandoned. ‘It’s a piece of data which isn’t often known,’ explains Jean-Paul Kasprzyk. ‘In the present case, the vehicle’s owner remembered the mileage at the time the car was stolen. We could thus deduct that the criminal gang had travelled approximately 100 kilometres in four days.’

On the basis of this data the researchers registered the cartography of the region in a numerical model, established the most plausible scenarios of the trajectories travelled, and put forward the hypothesis of the existence of a withdrawal zone. The final stage was to point out different locations where there was a chance this zone could be located.

Vector method and raster method

There exist two ways of storing and utilising geographic data numerically. The vector method and, which was the method used in this study, the raster method, which consists of cutting up an image into several information units, cells, or pixels. 

Raster method has a slight disadvantage, being heavier than the vector method. ‘In a vector approach, we only define the objects which are of interest to us,’ says Jean-Paul Kasprzyk. ‘In an image all the territory is represented, and each pixel must contain information, a value. In the case of roads, for example, a simple binary value is enough to mark the layout of the roads in the image’ (see illustration below).

So why use the raster method, if it is heavier than the vector method? Simply because this approach offers alternative but complementary possibilities in terms of data processing vis-à-vis the vector approach. ‘We privileged it for two reasons,’ explains Marie Trotta, co-author of the publication. ‘First of all because it allows the application of propagation algorithms. Propagation means that passing from one pixel to another will increase the value of the itinerary by a process of addition. As if each pixel had a value determined beforehand. To pass from one pixel to another, you have to ‘pay’.’ For example, in the context of this study, the resolution of each pixel corresponds to 20 metres by 20. On moving from one pixel to another next to it, one crosses a cost surface of 20 metres. The cumulated value of the second pixel is thus 40 metres. Normally, a propagation can be carried out in any direction starting from the original pixel. Yet the criminals had a car. To calculate their trajectory the researchers had to use the road network. In adding this network restriction to the logic of propagation it thus became possible to calculate the shortest cumulated distance between each pixel of the network and the different sites the crimes took place.

The raster method has also enabled math-algebra techniques to be used. ‘For the same mapped region, and depending on the data we wish to highlight in the pixels, we have to produce several images,’ illustrates Jean-Paul Kasprzyk. ‘One image, for example, will be made up of pixels which record the layout of the roads. Another will present the values according to relief, yet another according to the situation of the pixels in an urban or a rural environment, etc. The possibilities are infinite. What the raster method enables you to do is to attribute values to each of these pixels according to what they represent, and to add, multiply or subtract, for example, these values amongst themselves in a multi-criteria model.’ This allows one to demarcate the search zones according to several factors studies. Imagine, for example, that during an investigation, one reckons that the criminal being looked for is hiding in a forest next to a water course and a road. In adding together the rasterised images presenting the proximity to the road networks and the rivers, and the location of the forests, it would be possible to only extract the pixels close to the roads, close to the rivers, and located inside a forest, and as a result orient the search according to these results.

Developing different scenarios...

Once the maps had been digitalised the criminals’ journey needed to be imagined. All in all four scenarios were suggested. The first was a simple adding up of the distances covered between the criminal events. A loop between the thefts and the car being abandoned. This loop only measured 86 kilometres. This scenario did not suit, thus, as the expected 100km had not been covered. The second scenario integrated a withdrawal zone, with a round trip between this landmark and each of the crime scenes.

In the third scenario, roughly similar, the gang did not pass by the withdrawal zone between the fourth event and the abandonment of the car. ‘This supposition arose from the fact that only four hours had passed between the last crime and the moment the police found the car,’ explains Marie Trotta. ‘It was too short a time lapse to imagine a withdrawal between the two events.’ A fourth scenario, finally, offered two round trips between the withdrawal zone and the second crime, in other words a robbery at a supermarket, thus explaining a possible prior reconnaissance of the site. But in adding on this extra round trip the possible routes greatly exceeded 100 kilometres. The researchers’ attention thus focused on the third scenario.

‘From this scenario,’ explain the two researchers, ‘different possible itineraries were established by adding up the cost surfaces in order to retain only pixels close to 100 kilometres as possible withdrawal sites. But we still had too many possible withdrawal sites, too many candidate pixels.’

…to discovering plausible withdrawal zones

To reduce the number of candidate pixels, it was thus necessary to integrate further data beyond that of distance. After consultation with the police, two other factors were taken into account. ‘When criminals choose a withdrawal zone, they tend to favour rural zones,’ explains Jean-Paul Kasprzyk. ‘They also privilege sites close to main roads, so that they can flee rapidly.’

A cartographic image was created for each of these factors, once again divided into pixels of 20 metres by 20. In the case of the image referring to the itineraries, the pixels which presented a withdrawal zone whose distance accumulated with the different crime scenes was close to 100km had the highest score. For the image representing proximity to main roads, the pixels closest to these roads also had a higher score. The same goes, finally, for the pixels in the image which position zones according to their rural character. Each of these factors, depending on their importance had a greater or lesser weight. Respecting the distance was the most important, followed by proximity to main roads, and finally, the rural character of the region. ‘We then added up the results of each of these images by offsetting the points according to their weight. The higher the value of the pixels, the greater the chance that the criminals had hidden their vehicle there.’ For basic information technology reasons the value of each pixel varied between 0 and 255.

The search had nevertheless not yet been completed. Once again following a discussion with the police it turned out that the pixels had to accommodate a built up area. In all likelihood the criminals had needed a place to hide (garage, house, hangar, etc.). If this constraint was respected the pixel was validated. If not, it was discarded. This was technically possible thanks to a simple question of arithmetic. Whether or not a pixel contained a built up zone was differentiated in a binary manner. In the case were nothing had been built the pixel obtained a value of 0. In the opposite case it was accorded the value of 1. The three added up factors were thus multiplied by the constraint. The sum of a figure multiplied by 0 is always equal to 0. The cells which obtained a zero score were ruled out. As for the pixels with the best scores, they were extracted and represented the zone to be investigated. ‘In keeping only these cells, there remained only a small portion of road possible in the region studies,’ report the delighted researchers. ‘If we had not been in a simulation situation, we would have dispatched a police raid on the basis of these results.’

Helping to refine, and not resolve, the investigations

‘Once we had classed the pixels according to these criteria, we asked the police to provide us with the solution,’ says Marie Trotta. ‘It turned out that the pixel which housed the warehouse where the criminals hid had a value of 252 out of 255 on our map. It figured, based on our reasoning, amongst the most plausible withdrawal zones.’ In the present case, the geographical appraisal worked. But obviously it consists of an aid based on hypotheses, which cannot guarantee an absolute success rate. These types of information remain pathways to be explored.

A transposable approach

The data to which the researchers had access to certainly reflected a specific case. Each series of crimes has its unique characteristics, its clues and its unknowns. For example the unusual fact that the vehicle’s owner knew the mileage was a key piece of information to retrace the criminals’ route.

Whilst this methodology works for a very particular case, certain of its aspects are nonetheless transposable, and still little used in the classical approaches of cartographic profiling. And therein lies the main interest of such a search. ‘The management of real distance constraints is, for example, an important aspect of the approach,’ explains Marie Trotta. The calculation of the distances between the crimes could be studied in real distances, via the road network, notably through the propagation technique. This technique is obviously usable in the classic applications of profiling, even if the distance travelled by the vehicle is not known in advance. ‘It is for example possible to place as a constraint a minimisation of the sum of the distances, looking for the most rapid itinerary, or the most secure.’ The simple fact of working on the network, as elementary as it might appear, is also a wonderful innovation, allowing greater precision to be achieved. ‘Many applications work on Euclidean distances, in other words straight lines between two points,’ explains Jean-Paul Kasprzyk. ‘Yet when a criminal goes from a point A to a point B, he doesn’t cover this distance as the crow flies.’

The development of scenarios can also be transposed to other cases. This mechanism of thinking has, in the present case, systematised the use of the chronology of events and the possible interdependence between two activities which can arise from it. For example the short lapse of time between the final event and the discovery of the abandoned car enables the researchers to deduce that the crooks had not passed by the withdrawal site between these two moments.

‘In the end we based ourselves exclusively on the data specific to the investigation,’ conclude the researchers. ‘One of the limitations of current profiling is that people do not sufficiently base themselves on data specific to the investigation, but rather on a model which does not specially reflect the criminal’s behaviour. One criminal’s behaviour cannot be compared to that of another. Basing oneself on models developed from other investigations can only add further approximations.’

The study thus offers new pathways to be explored in crime mapping, moving towards greater precision in estimating a criminal’s itinerary. It certainly does not constitute a miracle remedy for investigators. But this method can nevertheless obtain good results with a greater possibility of success than more approximate classical methods. However, as far as operational cartographic profiling in Belgium is concerned, requests for help on the part of the forces of order remain few in number. And the radical scale taken up in the budgets will certainly not reverse the trend. But there is nonetheless no lack of individual initiatives, both in terms of research and certain police chiefs with a penchant for new technologies. All that remains for the Belgian geomaticians is to hope that our country aligns itself with the interest displayed by certain European and North American states for this booming scientific investigation. In the meantime, this methodology can be transposed to other case studies, such as the conservation of the environment, where it can help to calculate the ecological cost of certain forms of transport, or the routes taken by motor-driven vehicles in certain regions of the globe.

(1) J.P. Kasprzyk, M. Trotta, K. Broxham, J.P. Donnay, Reconstitution of the journeys to crime and location of their origin in the context of a crime series. A raster solution for a real case study, in Michael Leitner (Ed.), Crime Modeling and Mapping Using Geospatial Technologies, Springer, 2012