The table **visualizes the dimensions for cognitive dynamic scene understanding:**

It shows **time in horizontal direction** from the point ‘**now**’ (second column from left) over the **local time integral** (**one video cycle**, column 4) to larger times depending on the** overall mission or task** (right).

**3-D space in vertical direction** is similarly scaled from the point ‘**here**’ (second row from the top) over its **differential environment** (row 3) to the **spatial extension of a single object** (row 4) and to **larger spaces depending on the overall mission or task** (bottom right):

**Time derivatives**(column 3) are**deliberately avoided in the 4-D approach**(in recursive estimation in general) since differentiation leads to noise amplification for higher frequencies [d/dt (A ∙ sin(ωt) = A ∙**ω**∙ cos(ωt)]. Instead, ‘**expectations**’ are computed by**predicting states and measurements**for the next point in time (through smoothing integration of the cognitive dynamic model). Then, the errors between values predicted and those measured are computed; incrementing predicted object states in direction of the measured features (via ‘Jacobian elements’ [Dickmanns, Wuensche 1999; Dickmanns 2007]) avoids noise amplification and yields a least squares fit according to the model; for system elements of higher order, the derivatives are reconstructed automatically by the recursive fit.- In the two image dimensions, differential changes of edge directions (
**row 3**) can directly be measured and are important elements for 3-D shape interpretation (curvature) of objects; shape description in differential terms is more compact than in Cartesian coordinates (*e.g.*roads described by clothoid elements do not need the integration constants for pose). - Combining shape- and motion interpretation (
**row 4, yellow rectangle with column 4**) allows**spatio-temporal (4-D) reconstruction**of**n moving objects in parallel**[‘**central hub**’, element (4, 4)]. These objects constitute the base for situation assessment and decision making for**mission accomplishment**(**blue rectangle, lower right**). - In conjunction,
**the scene including the depth dimension**, lost in perspective projection for a single image, can be perceived over time (**motion stereo**). In connection with the own intentions, this yields the**situation**to be taken into account for**intelligent decision making**. - The mission to be performed determines the total temporal and spatial scales to be taken into account.

### References

**Dickmanns ED** (1997). Vehicles Capable of Dynamic Vision. Proc. 15th International Joint Conference on Artificial Intelligence (IJCAI-97), Vol. 2, Nagoya, Japan, pp 1577-1592. Abstract (with Introduction)

**Dickmanns ED, Wuensche HJ** (1999). Dynamic Vision for Perception and Control of Motion. In: B. Jaehne, H. Haußenecker and P. Geißler (eds.) Handbook of Computer Vision and Applications, Vol. 3, Academic Press, pp 569-620. Content and Introduction

**Dickmanns ED** (2007). Dynamic Vision for Perception and Control of Motion. Springer-Verlag, London. Content