Geometric shapes can be represented in a variety of different ways. A distancemap is a map from points to distances. This can be used as a shape representationwhich can be created through a process known as a distance transform. This the-sis project tests a method for three-dimensional distance transforms using frac-tional volume coverage. This method produces distance maps with subvoxel dis-tance values. The result which is achieved is clearly better than what would beexpected from a binary distance transform and similar to the one known fromprevious work. The resulting code has been published under a free and opensource software license. / <p>The developed code is available under a GPL license here https://gitlab.com/Emiluren/3d-distance-transform</p>

Distance field text rendering has many advantages compared to most other text renderingsolutions. Two of the advantages are the possibility  to scale the glyphs without losing the crisp edge and less memory consumption. A drawback with distance field text renderingcan be high distance field generation time. The solution for fast distance field text renderingin this thesis generates the distance fields by drawing distance gradients locally over the outlines of the glyphs. This method is much faster than the old exact methods for generating distance fields that often includes multiple passes over the whole image. Using the solution for text rendering proposed in this thesis results in good looking text that is generated on the fly. The distance fields are generated on a mobile device in less than 10 ms for most of the glyphs in good quality which is less than the time between two frames.

Knowing the shapes, sizes and positional relations between features in an image can be useful for different types of image processing.Using a Distance Transform can give us these properties as a Distance Map.There are many different variations of distance transforms that can increase accuracy or add functionality, two such transforms are the Anti-Aliased Euclidean Distance Transform and the Signed Euclidean Distance Transform.To get the benefits of both of these it is of interest to see if they can be combined and if so, how does it perform?Investigating the possibility of such a transform is the main object of this thesis. To create this combined transform a copy of the image was created and then inverted, both images are transformed and the resulting distance maps are combined into one.Signed distance maps are created for three transforms using this method. The transforms in question are, EDT, AAEDT and VAAEDT.All transforms are then evaluated using a series of images containing two randomly placed circles, the circles are created using simple Signed Distance Functions. The signed transforms work and the AAEDT performs well compared to the Signed Euclidean Distance Transform.These results were expected as a similar gap in results can be seen between the regular EDT and AAEDT.But, this transform is not perfect and there is room for improvements in the accuracy, a good start for future work. / Att känna till formen, storleken samt olika objekts position relativt till varandra i en bild kan vara användbart för olika former av bildanalys.En Distance Transform kan ge oss alla dessa egenskaper i form av en ny bild, en så kallad avståndskarta.Det finns flera olika transformer som producerar avståndskartor med olika egenskaper och precision, två exempel är Anti-Aliased Euclidean Distance Transform och Signed Euclidean Distance Transform.För att få den ökade precisionen av Anti-Aliased Euclidean Distance Transform och funktionaliteten från en dubbelriktad så är det relevant att undersöka om de går att kombinera och om det går, hur presterar den nya transformen?Att undersöka om detta är möjligt är huvudmålet med detta arbete. För att skapa denna kombinerade transform så kopieras och inverteras bilden som ska transformeras, både kopian och orginalet transformeras sedan och de resulterande avståndskartorna kombineras till ett resultat.Dubbelriktade avståndskartor skapas för tre transformer, Euclidean Distance Transform, Anti-Aliased Euclidean Distance Transform och Vector Anti-Aliased Euclidean Distance Transform.Alla tre transformer utvärderas sedan genom en serie testbilder innehållandes två slumpmässigt placerade cirklar, skapade med hjälp av vektormatematik. De dubbelriktade transformerna fungerar och resultaten är i linje med motsvarande resultat för enkelriktade transformer.Detta betyder dock inte att resultaten är perfekta, utan det finns utrymme för prestandavinster i precisionen, detta är därför en bra startriktning för framtida förbättringsarbete.

<p>This thesis shows the result from investigations of methods that use distance vectors when matching pictures. The distance vectors are available in a distance map made by the Euclidean Distance Transform. The investigated methods use the two characteristic features of the distance vector when matching pictures, length and direction. The length of the vector is used to calculate a value of how good a match is and the direction of the vector is used to predict a transformation to get a better match. The results shows that the number of calculation steps that are used during a search can be reduced compared to matching methods that only uses the distance during the matching.</p>

This thesis shows the result from investigations of methods that use distance vectors when matching pictures. The distance vectors are available in a distance map made by the Euclidean Distance Transform. The investigated methods use the two characteristic features of the distance vector when matching pictures, length and direction. The length of the vector is used to calculate a value of how good a match is and the direction of the vector is used to predict a transformation to get a better match. The results shows that the number of calculation steps that are used during a search can be reduced compared to matching methods that only uses the distance during the matching.