Leena Ikonen

Shortest routes on varying height surfaces using gray-level distance transforms

The distance transform on curved space (DTOCS) and its locally Euclidean modification weighted DTOCS (WDTOCS) calculate distances along gray-level surfaces. This article presents the Route DTOCS algorithm for finding and visualizing the shortest route between two points on a gray-level height map, and also introduces new distance definitions producing more accurate global distances. The algorithm is very simple to implement, and finds all optimal paths between the two points at once. The Route DTOCS is an efficient 2D approach to finding routes on a 3D surface. It also provides a more flexible solution to obstacle avoidance problems than the constrained distance transform.

Distance and nearest neighbor transforms on gray-level surfaces

This article presents an efficient priority pixel queue algorithm for calculating the distance transform on curved space (DTOCS), the corresponding nearest neighbor transform, and the new projection DTOCS (PDTOCS). The transforms provide tools for approximating distances and finding shortest paths on gray-level surfaces. Surface variation, or roughness, can also be measured.

Pixel queue algorithm for geodesic distance transforms

Geodesic distance transforms are usually computed with sequential mask operations, which may have to be iterated several times to get a globally optimal distance map. This article presents an efficient propagation algorithm based on a best-first pixel queue for computing the Distance Transform on Curved Space (DTOCS), applicable also for other geodesic distance transforms. It eliminates repetitions of local distance calculations, and performs in near-linear time.

Priority pixel queue algorithm for geodesic distance transforms

The sequential mask operations for calculating distance transforms may have to be iterated several times in the case of geodesic distances. This article presents an efficient propagation algorithm for the Distance Transform on Curved Space (DTOCS). It is based on a best-first pixel queue, and is applicable also for other gray-level distance transforms. It eliminates repetition of local distance calculations, and performs in near-linear time. A nearest neighbor transform based on distances along the surface, and a propagation direction image for tracing the shortest paths, can be produced simultaneously with the distance map.

Distance transforms on anisotropic surfaces for surface roughness measurement

The Distance Transform on Curved Space (DTOCS) calculates distances along a gray-level height map surface In this article, the DTOCS is generalized for surfaces represented as real altitude data in an anisotropic grid The distance transform combined with a nearest neighbor transform produces a roughness map showing the average roughness of image regions in addition to one roughness value for the whole surface The method has been tested on profilometer data measured on samples of different paper grades The correlation between the new method and the arithmetic mean deviation of the roughness surface, Sa, for small wavelengths was strong for all tested paper sample sets, indicating that the DTOCS measures small scale surface roughness.

Distance and nearest neighbor transforms of gray-level surfaces using priority pixel queue algorithm

This article presents a nearest neighbor transform for gray-level surfaces. It is based on the Distance Transform on Curved Space (DTOCS) calculated using an efficient priority pixel queue algorithm. A simple extension of the algorithm produces the nearest neighbor transform simultaneously with the distance map. The transformations can be applied for example to estimate surface roughness.

Using external knowledge in neural network models

One of the most important properties of neural networks is generality, as the same network can be trained to solve rather different tasks, depending on the training data. This is also one of the most prominent problems when practical real world problems are solved by neural networks, as existing domain knowledge is difficult to incorporate into the models. In this contribution we present methods for adding prior knowledge to neural network modeling. The approach is based on training the knowledge on the network of hard-coding the knowledge in advance to the connections or weights. The knowledge is specified as target values or constraints for different order partial derivatives of the network. This approach can be viewed as a flexible regularization method that controls directly the characteristics of the resulting mapping. The proposed algorithms have been implemented in a neural network modeling tool that supports modular network design and domain knowledge representation with fuzzy-like terms. In this paper we present examples of the effect of incorporating different degrees of information from the modular structure and the functional behavior of the target processes in the model building and training.

Shortest route on gray-level map using distance transform on curved space

The Distance Transform on Curved Space (DTOCS) can be used to calculate distances on a gray-level surface, but the route along which the shortest distance is found, is lost during the calculation. In this article a new method for finding and visualizing the shortest path between two points on a gray-level height map is presented. The method is simple to implement, and example route images show that it produces good results.

Shortest Route on Height Map Using Gray-Level Distance Transforms

This article presents an algorithm for finding and visualizing the shortest route between two points on a gray-level height map. The route is computed using gray-level distance transforms, which are variations of the Distance Transform on Curved Space (DTOCS). The basic Route DTOCS uses the chessboard kernel for calculating the distances between neighboring pixels, but variations, which take into account the larger distance between diagonal pixels, produce more accurate results, particularly for smooth and simple image surfaces. The route opimization algorithm is implemented using the Weighted Distance Transform on Curved Space (WDTOCS), which computes the piecewise Euclidean distance along the image surface, and the results are compared to the original Route DTOCS. The implementation of the algorithm is very simple, regardless of which distance definition is used.