A persistence lens is a hierarchy of disjoint upper and lower level sets of a continuous luminance image's Reeb graph. The boundary components of a persistence lens's interior components are Jordan curves that serve as a hierarchical segmentation of the image, and may be rendered as vector graphics. A persistence lens determines a varilet basis for the luminance image, in which image simplification is a realized by subspace projection. Image scale space, and image fractal analysis, result from applying a scale measure to each basis function.
The ultimate goal of this indoor mapping research is to automatically reconstruct a floorplan simply by walking through a house with a smartphone in a pocket. This paper tackles this problem by proposing FloorNet, a novel deep neural architecture. The challenge lies in the processing of RGBD streams spanning a large 3D space. FloorNet effectively processes the data through three neural network branches: 1) PointNet with 3D points, exploiting the 3D information; 2) CNN with a 2D point density image in a top-down view, enhancing the local spatial reasoning; and 3) CNN with RGB images, utilizing the full image information. FloorNet exchanges intermediate features across the branches to exploit the best of all the architectures. We have created a benchmark for floorplan reconstruction by acquiring RGBD video streams for 155 residential houses or apartments with Google Tango phones and annotating complete floorplan information. Our qualitative and quantitative evaluations demonstrate that the fusion of three branches effectively improves the reconstruction quality. We hope that the paper together with the benchmark will be an important step towards solving a challenging vector-graphics reconstruction problem. Code and data are available at https://github.com/art-programmer/FloorNet.