# Thiago Pereira 's Research

## RGBN Image Editing

[T. Pereira and L. Velho]We propose a method to edit RGBNs (images with a color and a normal channel). High resolution RGBNs are easy to obtain using photometric stereo. Free editing will result in normals which do not correspond to any realizable surface. Our normal operators guarantee the integrability of the results. Our method can filter normals with any linear kernel allowing high-pass and edge-enhancement filters. We have designed a normal linear combination method for adding details with frequency control. New geometric features can be created with a custom brush that warps deformations along its path. A nonlinear operator is also proposed. Its integrability is controlled with a two-band separation of frequencies: smooth shape and details. [ pdf ] [ html ] [ presentation ]

Thiago Pereira and Luiz Velho.

**"RGBN image editing"**. In Proceedings of SIBGRAPI, 2009.

## Symmetry-Based Completion

[T. Pereira and R. Paes Leme]Acquired images often present missing, degraded or occluded parts. Inpainting techniques try to infer lacking information, usually from valid information nearby. This work introduces a new method to complete missing parts from an image using structural information of the image. Since natural and human-made objects present several symmetries, the image structure is described in terms of axial symmetries, and extrapolating the symmetries of the valid parts completes the missing ones. In particular, this allows inferring both the edges and the textures. [ pdf ] [ html ] [ presentation ]

Thiago Pereira, Renato Paes Leme, Luiz Velho, and Thomas Lewiner.

**"Symmetry-based Completion"**. In Proceedings of GRAPP 2009, 2009.

## Centroidal Voronoi Tesselations

### Computational Geometry // Fall 2008

[T. Pereira and L. Sacht]CVTs are Voronoi Tessellations whose generating points are the centroids of the corresponding Voronoi Regions. They have applications in image compressing, quadrature rules, remeshing and segmentation of surfaces. Their extensions to general spaces are also available. In this work we have implemented CVTs on surfaces represented by triangular meshes. We also explore the ideas of Variational Shape Approximations (VSA) for Normal Clustering and mix these ideas with CVT's. Different densities and metrics are used, derived from normals, curvatures and geodesics. [ html ] [ presentation ]

## Completing Missing Regions using Symmetries

### Reconstruction Methods // Fall 2007

[T. Pereira and R. Paes Leme]Symmetries are a very important aspect of many natural and human-made objects. They are common in many fields like arts, architecture, mathematics and design. A shape is symmetric if there is a transformation that maps the shape onto itself. In this work, we restrict our attention to reflective symmetries. Most symmetries that are found are not perfect. Also, some symmetries only hold in a subset of the object. These are called partial symmetries. This motivates research for algorithms that identify partial and approximate symmetries. We have implemented a symmetry detection scheme largely based on the work of Mitra et al. We develop an application of symmetry detection: completion of missing regions in objects. [ html ]

## Medial Axis Reconstruction

### Reconstruction Methods // Fall 2007

[T. Pereira and R. Paes Leme]The Medial Axis of a shape is composed by the points whose distance to the shape is realized by more than one point. There are known methods to calculate the medial axis of polygons, polynomial curves and some other special shapes. One important problem in the Field of 3D Reconstruction is estimating the medial axis of a shape represented by a point cloud. It is known that the medial axis is a subset of the Voronoi diagram. A classic approach is to calculate the diagram and to filter the Voronoi facets. This approach is not robust in face of noise and outliers. In this work, we counter this problems by calculating the medial axis through random sampling of the point cloud. [ html ]

## Edge-search Number in Graphs with many Symmetries

### BEng Thesis // 2007

[R. Paulino, R. Paes Leme and T. Pereira]We give an algorithm for the Edge-Search Number problem. It consists on finding the minimum number of searchers to capture a fugitive that moves along the edges of a graph G. It is known to be NP-Complete. The algorithm is based on a Dijkstra search through a state space. We propose pruning the search using information from the graph's group of automorphisms.

Rafael Paulino, Renato Paes Leme, Thiago Pereira, and Claudia Justel.

**Edge-search-number in graphs with many automorphisms**[ in Portuguese ], SBPO 2007, XXXIX SBPO, 2007, Fortaleza. Anais do XXXIX Simposio Brasileiro de Pesquisa Operacional, 2007.