Overall Objectives
Research Program
Application Domains
Bilateral Contracts and Grants with Industry
Partnerships and Cooperations
Bibliography
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## Section: New Results

### Analysis

#### Planar Shape Detection and Regularization in Tandem

Participants : Sven Oesau, Florent Lafarge, Pierre Alliez.

We contributed a method for planar shape detection and regularization from raw point sets. The geometric modeling and processing of man-made environments from measurement data often relies upon robust detection of planar primitive shapes. In addition, the detection and reinforcement of regularities between planar parts is a means to increase resilience to missing or defect-laden data as well as to reduce the complexity of models and algorithms down the modeling pipeline. The main novelty behind our method is to perform detection and regularization in tandem. We first sample a sparse set of seeds uniformly on the input point set, then perform in parallel shape detection through region growing, interleaved with regularization through detection and reinforcement of regular relationships (coplanar, parallel and orthogonal). In addition to addressing the end goal of regularization, such reinforcement also improves data fitting and provides guidance for clustering small parts into larger planar parts (Figure 1 ). We evaluate our approach against a wide range of inputs and under four criteria: geometric fidelity, coverage, regularity and running times. Our approach compares well with available implementations such as the efficient RANSAC-based approach proposed by Schnabel and co-authors in 2007 [8] . This work has been published in the Computer Graphics Forum journal.

Figure 1. Shape detection and regularization. The input point set (5.2M points) has been acquired via a LIDAR scanner, from the inside and outside of a physical building. 200 shapes have been detected, aligned with 12 different directions in 179 different planes. The cross section depicts the auditorium in the upper floor and the entrance hall in the lower floor. The closeup highlights the steps of the auditorium which are made up of perfectly parallel and orthogonal planes.

#### Image partitioning into convex polygons

Participants : Liuyun Duan, Florent Lafarge.

In collaboration with Geoimage

The over-segmentation of images into atomic regions has become a standard and powerful tool in Vision. Traditional superpixel methods, that operate at the pixel level, cannot directly capture the geometric information disseminated into the images. We propose an alternative to these methods by operating at the level of geometric shapes. Our algorithm partitions images into convex polygons. It presents several interesting properties in terms of geometric guarantees, region compactness and scalability. The overall strategy consists in building a Voronoi diagram that conforms to preliminarily detected line-segments, before homogenizing the partition by spatial point process distributed over the image gradient. Our method is particularly adapted to images with strong geometric signatures, typically man-made objects and environments (Figure 2 ). We show the potential of our approach with experiments on large-scale images and comparisons with state-of-the-art superpixel methods [17] . This work has been published in the Computer Graphics Forum journal. Published in the proceedings of CVPR (IEEE conference on Computer Vision and Pattern Recognition).

Figure 2. Image partitioning into convex polygons.

#### Object Classification via Planar Abstraction

Participants : Sven Oesau, Florent Lafarge, Pierre Alliez.

Figure 3. Classification. Left: We used four tabletop object classes from the Princeton Shape Benchmark: Bottle, Lamp, Mug and Vase. We also select four furniture object classes common to indoor scenes: Chair, Couch, Shelf and Table. Right: We evaluate our approach through computing a confusion matrix, for an increasing amount of noise and outliers. (a): Without noise and outliers. The precision of the class prediction is $82,5%$. The classifier is not reliable for classifying the bottles, which get mislabeled as vases. (b): Added $10%$ outliers and $0.5%$ noise. Compared to the noise-free version the precision slightly dropped to $77.5%$. (c): Added $20%$ outliers and $1%$ noise. The method maintains a precision of $70%$ for this level of noise.

#### Optimizing partition trees for multi-object segmentation with shape prior

Participants : Emmanuel Maggiori, Yuliya Tarabalka.

This work has been done in collaboration with Dr. Guillaume Charpiat (TAO team, Inria Saclay).

Partition trees, multi-class segmentation, shape priors, graph cut.

A partition tree is a hierarchical representation of an image. Once constructed, it can be repeatedly processed to extract information. Multi-object multi-class image segmentation with shape priors is one of the tasks that can be efficiently done upon an available tree. The traditional construction approach is a greedy clustering based on color similarities. However, not considering higher level cues during the construction phase leads to trees that might not accurately represent the underlying objects in the scene, inducing mistakes in the later segmentation. We proposed a method to optimize a tree based both on color distributions and shape priors [15] . It consists in pruning and regrafting tree branches in order to minimize the energy of the best segmentation that can be extracted from the tree. Theoretical guarantees help reduce the search space and make the optimization efficient. Our experiments (see Figure 4 ) show that we succeed in incorporating shape information to restructure a tree, which in turn enables to extract from it good quality multi-object segmentations with shape priors. Published in the proceedings of BMVC (British Machine Vision Conference).

Figure 4. Classification results for the satellite image over Brest. $𝒜$ denotes overall classification accuracy, and $𝒟$ denotes average buildings overlap. The performance of the proposed binary partition tree (BPT) optimization method is compared with the following methods: 1) support vector machines (SVM) classification; 2) graph cut (GC) with $\alpha$-expansion; 3) cut on the BPT, regularized by the number of regions without using shape priors (TC).