Computer vision discretizes space in pixels and then proposes approaches (i.e. segmentation, edge detectors, feature detectors, etc.) to arrange those pixels together again in order to detect objects and to describe them inside space by naming its location, topology, distance, etc. in a scene. As the basics in computation are the discretization of continuous signals (i.e. Boolean calculus, light waves represented in colour coordinates, etc.), properties of the space must be reminded to students when teaching computer vision from a spatial cognition perspective. Psychological spatial thinking tests help students to remind which abilities they use to solve spatial problems such as inferring cross sections or canonical views of a 3D object, which are common problems in industrial design engineering or computer-aided design (CAD) tasks. According to our experience, Qualitative Spatial and Temporal Reasoning methods provide students with tools to represent space and its continuous transformations, which enable them to define approaches closer to spatial cognitive reasoning.
Fig. 1. Image of a scene represented as a matrix of pixels Red Green and Blue (RGB), then
segmented by the boundary extraction method by Canny [
(a) Original image
(b) Point clouds
(c) Object recognition
edge parallelism [
What can we learn from spatial cognition research that we can apply to computer vision and computer systems in general, so that the process of interacting with space is more ‘intelligent or intuitive’?
In my teaching classes, spatial cognition is introduced from the point of view of
spatial problem solving. Students in computer science get surprised when I ask them
to answer some psychological tests on: (i) diagrammatic representations, translation
from 3D to 2D and viceversa [
After carrying out these tests, students realize some of the skills required in spatial problem solving. Then they are required to define logical approaches to solve these spatial problems. In their bachelor degree, they acquire knowledge about the digitalized information that computer systems get. So, they must think out of the box to identify ways to solve ‘spatial-analog’ problems in a digitalized world. Some of the properties students get aware of after solving the spatial problems are: – Abstraction: people abstract dimensions in space (i.e. by assuming one dimension as constant) and re-represent data in a way that helps visualizing a problem to solve. For example, a map of the Earth represents 3D space in a 2D paper, sometimes assuming relief or altitude as constant. – Continuity: dimensions in space are continuous. Although they can be abstracted or considered as constant in a representation, this representation must be coherent with the space and transmit changes in the dimension abstracted, if produced. If a change in relief is produced (i.e. a road is cut), this change should be transmitted to all dimensions and the map should represent this discontinuity. – Relativity: most dimensions in space are relative or inter-related to each other. For example, when comparing roads in a map, if the roads are represented by abstracting the same dimension, then they can be compared directly. If one road considers relief while the other does not, then they are not comparable.
Qualitative Reasoning methods is also introduced to students by Allen’s model of temporal relations which is very useful to introduce continuity and reasoning constraints in time which then we can extrapolate to space by explaining the notion of conceptual neighbourhood in common space [16] and in other spaces, such as colour spaces [17]. 3
Result Example: Qualitative Description of Objects using Depth The result of teaching spatial thinking related to computer vision and to qualitative modelling leaded to the definition of a model for 3D object description which takes into account depth in the 3 canonical perspectives of the object at the same time [18] (see Fig. 3). Thus, it propagates changes in object volume, and it can also identify inconsistent descriptions. Further evaluation is needed to study how cognitive is the proposed model.
The COGNITIVE-AMI1 project (GA 328763) funded by EU-FP7 Marie Curie IEF actions and the Cognitive Qualitative Descriptions and Applications2 (CogQDA) project funded by Universita¨t Bremen are acknowledged. Also the support by the Bremen Spatial Cognition Center3 (BSCC) and the EU Erasmus+ Staff Mobility for Teaching program are acknowledged.
1https://sites.google.com/site/cognitiveami/ 2https://sites.google.com/site/cogqda/ 3http://bscc.spatial-cognition.de/ 13. Hegarty, M., Keehner, M., Khooshabeh, P., Montello, D.R.: How spatial abilities enhance, and are enhanced by, dental education. Learning and Individual Differences 19(1) (2009) 61–70 14. Keehner, M., Hegarty, M., Cohen, C.A., Khooshabeh, P., Montello, D.R.: Spatial reasoning with external visualizations: What matters is what you see, not whether you interact.
Cognitive Science 32(7) (2008) 1099–1132 15. Maeda, Y., Yoon, S.Y., Kim-Kang, K., Imbrie, P.K.: Psychometric properties of the revised psvt:r for measuring first year engineering students spatial ability. International Journal of Engineering Education 29 (2013) 763–776 16. Freksa, C.: Temporal reasoning based on semi-intervals. Artificial Intelligence 54(1–2) (1992) 199 – 227 17. Falomir, Z., Museros, L., Gonzalez-Abril, L.: A model for colour naming and comparing based on conceptual neighbourhood. an application for comparing art compositions.
Knowledge-Based Systems 81 (2015) 1–21 18. Falomir, Z.: A qualitative model for reasoning about 3d objects using depth and different perspectives. In T. Lechowski, P. Waga, M.Z., ed.: LQMR 2015 Workshop. Volume 7 of Annals of Computer Science and Information Systems., PTI (2015) 3–11