Biological vision and computer vision cannot be treated independently anymore. The digital revolution and the emergence of more and more sophisticated technical applications caused a symbiosis between the two communities. Competitive technical devices challenging the human performance rely increasingly on algorithms motivated by the human vision system. On the other hand, computational methods can be used to gain a richer understanding of neural behavior, e.g. the behavior of populations of multiple processing units. The relations between computational approaches and biological findings range from low level vision to cortical areas being responsible for higher cognitive abilities. In early stages of the visual cortex cells have been recorded which could not be explained by the standard approach of orientation- and frequency-selective linear filters anymore. These cells did not respond to straight lines or simple gratings but they fired whenever a more complicated stimulus, like a corner or an end-stopped line, was presented within the receptive field. Using the concept of intrinsic dimensionality, these cells can be classified as intrinsic-two-dimensional systems. The intrinsic dimensionality determines the number of degrees of freedom in the domain which is required to completely determine a signal. A constant image has dimension zero, straight lines and trigonometric functions in one direction have dimension one, and the remaining signals, which require the full number of degrees of freedom, have the dimension two. In this term the reported cells respond to two dimensional signals only. Motivated by the classical approach, which can be realized by orientation- and frequency-selective Gabor-filter functions, a generalized Gabor framework is developed in the context of second-order Volterra systems. The generalized Gabor approach is then used to design intrinsic two-dimensional systems which have the same selectivity properties like the reported cells in early visual cortex. Numerical cognition is commonly assumed to be a higher cognitive ability of humans. The estimation of the number of things from the environment requires a high degree of abstraction. Several studies showed that humans and other species have access to this abstract information. But it is still unclear how this information can be extracted by neural hardware. If one wants to deal with this issue, one has to think about the immense invariance property of number. One can apply a high number of operations to objects which do not change its number. In this work, this problem is considered from a topological perspective. Well known relations between differential geometry and topology are used to develop a computational model. Surprisingly, the resulting operators providing the features which are integrated in the system are intrinsic-two-dimensional operators. This model is used to conduct standard number estimation experiments. The results are then compared to reported human behavior. The last topic of this work is active object recognition. The ability to move the information gathering device, like humans can move their eyes, provides the opportunity to choose the next action. Studies of human saccade behavior suggest that this is not done in a random manner. In order to decrease the time an active object recognition system needs to reach a certain level of performance, several action selection strategies are investigated. The strategies considered within this work are based on information theoretical and probabilistic concepts. These strategies are finally compared to a strategy based on an intrinsic-two-dimensional operator. All three topics are investigated with respect to their relation to the concept of intrinsic dimensionality from a mathematical point of view
