CaS: Collection-aware Segmentation

Transcription

1 CaS: Collection-aware Segmentation Raquel Costa Manuel J. Fonseca Alfredo Ferreira INESC-ID/IST/Technical University of Lisbon Lisboa Abstract Ao longo dos tempos, a segmentação tem provado ser um desafio devido à sua subjectividade. A segmentação depende não apenas do domínio em causa mas acima de tudo da interpretação que os humanos fazem do objecto. Para cada contexto, diversas soluções específicas foram propostas com diferentes objectivos, limitações e vantagens. Neste trabalho propomos ultrapassar algumas dessas limitações usando o algoritmo de segmentação Collection-aware Segmentation (CaS). Este algoritmo identifica segmentos de objectos em colecções baseados na sua individualidade nessa colecção. Para esse efeito realizámos um conjunto de testes para compreender como as pessoas segmentam objectos numa colecção. A partir dos resultados destes testes desenvolvemos os algoritmos Adaped-CaS e Geons-augmented CaS. Avaliações experimentais com utilizadores mostraram que a abordagem proposta produz segmentações com significado para os humanos. Abstract Segmentation has always proven to be a challenge because of its subjectiveness. It depends not only of application domain but also most on human interpretation. To each context, several specific solutions were proposed with different goals, limitations and advantages. With this work we propose to overcome some of those limitations by improving Collection-aware Segmentation algorithm (CaS). This algorithm identifies segments of objects in collections based on ir individuality among collection in which objects belong. To that end we performed a set of tests to understand how humans segment a collection of objects. From results of se tests we developed Adaped-CaS and Geons-augmented CaS algorithms. Experimental evaluation with users revealed that our approach produces a segmentation that is meaningful for humans. Keywords 3D Object Segmentation, 3D Object Collections, Automatic Segmentation, Similarity Estimation 1. Introduction Each human being interprets environment from his own point of view. This generates an huge range of possible interpretations of world, and his components. Thus, segmentation of objects may vary from individual to individual. Indeed, it and has been subject of studies in different areas, from mamatics to philosophy. Over past decades object segmentation has been also tackled within computer graphics domain, as a result of growing number of 3D objects in digital format and widespread of applications that use m. Many computer graphics applications, as animation, collision detection, object indexing and retrieval use segmentation approaches as a stage of core process. However, most of existing object segmentation techniques are domain or context dependent. These perform well in domain and context for which y were designed for, but not so good in or domains or contexts. To overcome this limitation we adopt a different approach that extends Collection Aware Segmentation (CaS) method. This was originally proposed in [Ferreira 09] embedded in a solution for indexing and retrieval of 3D objects. In this paper we extend CaS to make it a stand-alone segmentation technique that produces meaningful results to users, independently of object domain. With present work we isolated CaS approach of indexing and retrieval application, thus creating a segmentation algorithm that is application independent. As original CaS approach, Adapted CaS is based on Hierarchical Fitting Primitives [Falcidieno 06] algorithm and uses Spherical Harmonics shape descriptor [Kazhdan 03]. By adding geon analysis [Biederman 87], we improved algorithm, achieving better segmentation, closer to human perception. To evaluate proposed approach, we conducted an experimental evaluation where several tests were performed. The first test focusing on understanding how humans segment 3D objects. From results of this test we devel-

2 Figure 1. Two different types of segmentation: a) Part Based Segmentation; b) Surface Based Segmentation. (Figure taken from [Shamir 08]) oped and refined our approach. Then, to evaluate efficacy and effectiveness of approach we executed performance tests to study execution time and memory requirements. Finally, to validate quality of segmentation, we organized a test where users where asked to compare results of manual segmentation made by humans with results produced automatically by segmentation algorithms. In remaining of this document we start with a brief presentation of related work on three-dimensional object segmentation. Then we describe original Collection Aware Segmentation algorithm, followed by its evolution and explanation on detail of how se work. On section 4 we describe evaluation tests and discuss corresponding results. In last section, we present conclusions of this work and reflect on future research paths on this topic. 2 Related Work 2.1 Categorization of segmentation approaches Some authors [Agathos 07, Shamir 08] classify segmentation techniques in two categories depending on kind of segmentation accomplished, represented in Figure 1. The part based segmentation is closer to user perception and divides object into sub-components, while surface based segmentation are accomplished by analysing surface shape features. Among se two types, 3D object segmentation has been widely studied and different solutions that uses distinct approaches have been proposed. Some of existing and more relevant are presented next. 2.2 Region Growing and Clustering The region growing methodology follows a exploratory approach that starts by visiting a seed (a face of mesh), n agglomerates adjacent faces by transversing mesh and it stops when it reaches a stop condition. Such Figure 2. Hierarchical decomposition with fuzzy area represented in red. (Figure taken from [Katz 03]) condition can be segment convexity. Then process is restarted using a non visited face as a new seed. The approach proposed by Zuckerberger on [Zuckerberger 02], uses a depth first or breadth first search to transverse a graph that represents mesh and seed where it starts is a node of this graph. From this transverse is creates a segment and n, it restarts transversing on an unvisited node of graph forming a new segment. In a similar way, Attene et al. [Falcidieno 06] approach also agglomerates faces, but instead of creating patch by patch, it creates all patches simultaneously. These are organized as an hierarchical tree in which leafs are mesh triangles and root is entire object. This tree is built bottom to top and clusters adjacent faces with minimum merging cost that can be calculated on different ways. Attene et al. uses primitives by fitting m to resultant cluster. Previously, Katz and Tal [Katz 03] had proposed to generate, in an iterative clustering, various results of segmentation given a number of clusters, and n chooses which is best segmentation. It starts by creating a representative group of clusters and n each adjacent face is clustered until it reaches a ray r between seed and limit of patch. This is used to agglomerate faces that have more probability of belonging to a given segment, thus creating fuzzy areas, illustrated Figure 2. Lastly it is needed to transform fuzzy decomposition in a final decomposition by refining limits. 2.3 Skeleton Based This approach uses skeleton of object to determine segmentation. The most used method to extract skeleton is Reeb Graph. For instance, Tierny et al. [Tierny 07] extract an enhanced topological skeleton by finding feature points located on object extremities using geodesic distances. These are used to create a function that indicates distance from a given point of mesh to each feature point of mesh and from re is built Reeb graph. After having skeleton, object is seg-

3 mented in areas where each skeleton node corresponds to a segment of object. 2.4 Geometry and Structure-Based The Taylor and Plumber algorithms, by Mortara et.al. [Mortara 03] uses object shape to perform segmentation based on geometry and structure. These algorithms detects tubular features by blowing bubbles that starts on a seed that is predefined and stops blowing when it finds an abrupt change on object shape, such as a bifurcation. Later, Mortara et al. [Mortara 06] used Plumber approach to find tubular zones in objects that represents human body. 2.5 Feature Points and Core Extraction In an attempt to overcome pose invariant limitation a new approach arises called Feature Points and Core Extraction that was proposed by Katz et al. in [Katz 05]. This initially creates a pose invariant representation of object, n extracts feature points and core. After finding core it is necessary to extract rest of segments which is done by matching each part to feature points. In end, it reverse initial process so object can come back to same shape. 2.6 SDF A different approach was proposed by Shapira et al. in [Shapira 08]. They use shape diameter function (SDF) for segmenting objects. In short, this gives diameter of an object in a neighbour of a point and is used to merge points that have same or close diameter values using a histogram. 2.7 Automatic Segmentation of 3D Collections The above referred approaches, as most existing approaches, segment 3D objects individually. The segmentation is performed object by object individually, instead of segmenting various objects simultaneously. Indeed, this is a relatively recent concept: to accomplish automatic simultaneous segmentation of sets of objects. The approaches that use automatic segmentation of 3D collections use information of similar objects to improve results. The group of Thomas Funkhouser in Priceton is one of groups that is already studying this subject. They presented an algorithm [Golovinskiy 09] that builds a graph whose nodes represents mesh faces and edges represents edges of mesh that connects adjacent faces of same object. They also represent correspondence between faces of different meshes. In next step algorithm executes a hierarchical clustering of graph, were adjacent faces of same model, and correspondent faces of different models are going to probably belong to same segment. 2.8 Discussion Several segmentation approaches have emerged as decomposition of 3D objects as is used in many different applications in distinct domains that require different segmentations. This also makes task of evaluating approaches hard to perform, due due large number of approaches. Neverless, Funckhouser and his team defined a benchmark for 3D mesh segmentation [Chen 09], compared seven mesh segmentation algorithms and draw some interesting conclusions. However, a common limitation is need of inputs provided by users in order to decompose objects. Some need to predefine seeds like in Region Growing and Iterative Clustering Approaches. Ors to select level of hierarchy generated by segmentation approach, se are all approaches that produce a hierarchical segmentation. The result of segmentation has more segments that it should have producing over segmented result. Some approaches try to overcome this limitation by using post-processing stage that removes extra segments by merging m to ors or by initially predefining a maximum number of segments. The individual segmentation of objects can be considered a limitation if we consider segmenting a collection of objects. If segmentation decomposes object by object as it is in major approaches, n it can take more time to decompose entire collection than if segmentation was performed simultaneously. In order to overcome limitations highlighted above, we propose a different solution based on CaS algorithm, presented in next section. This is a segmentation approach that will be application independent. 3 Collection-aware Segmentation In this section we present a distinct approach for segmenting 3D objects whose main goal is to overcome some limitations found on existing approaches. We extracted Collection-aware Segmentation (CaS) algorithm from indexing and retrieval context where it was embedded [Ferreira 09], as a step of a complete solution, and extended it to a fully fledged 3D object segmentation algorithm. This led to original CaS and to evolution for Geons-Augmented CaS. 3.1 Original CaS for Retrieval The original CaS, integrated in a retrieval solution, did not indeed produced any object segmentation per se. Instead, it decomposes all objects in a collection and stores ir subparts in a shape pool, used n for indexing collection. This approach, depicted in Figure 3 has two main stages: initialization stage and iteration stage. In first stage foundations of segmentation are computed and loaded into memory, while in following stage objects of collection are iteratively segmented into subparts. The initialization starts by generating, for each object on collection respective hierarchical segmented mesh (HSM) using Hierarchical Fitting Primitives (HFP) as proposed by Attene et al. [Falcidieno 06]. This approach consists on merging clusters and n fitting m to primitives to create final clusters. Next it saves resulting HSM on HSM Set, producing a set of segmented meshes. Then is computed for each mesh, ob-

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5 NDL Minimal TriCount Reached? Not NO K-WR Singular? Figure 7: 6. Decomposition fluxogram fluxogram of adaptedofcas Adapted CaS. sponds to Archa level onbarrel hierarchy. In order to support Cylinder Cone segmentation, iteration stage uses NDL. In practice, each iteration of stage is an iteration to NDL. So, this stage starts on first element of NDL and verifies if is decomposable or not. Cube Ex-Cylinder Ex-Handle Handle To segment objects based on collection where y belong, it is necessary to compare each sub-part with all or sub-parts. Figure 6 illustrates steps for labelling a segment Ex-Pyramidas decomposable Pyramid or Plan not. It first verifies Wedge if has reached minimal triangle count by calculating number Figure of triangles 8: Example between ofboth group child of nodes geonsand used compares on Geons-augmented approach this with a previously defined value - minimum triangle count. 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If result is segment being decomposable, n it is going to decompose it, for that, it goes to respective Figure HSM9: and Decomposition get his child nodes. fluxogram After having of geons child augmented it calculates CaS ir respective signatures, adds m nodes, to signature pool and insert both nodes on Non Segmented List (NSL), this list contains segments that are going to be processed on next iteration and removes processed element from NDL passing to next ele- NO In order to compare segments to geons it is necessary to predefine best similar values between m. So, best values for similarity thresholds between segments and geons where studied. To compare objects it is used, as was already referred, Spherical Harmonics (SHA). One is that y are not scale invariant, that is, it takes into account scale when comparing to objects, using difference between signatures. So, it was not only necessary to discover best similarity threshold for usual geons but also a profound study about different scales and different smooth variations on geons to really overcome this problem of scale invariance. To overcome this limitation a study was performed on cylinder, for that, is was used several different types of cylinders. In Figure 10 are represented different variations of cylinders, first row are cylinders that are closed both on top as on bottom. The middle row are Figure 7. Group of geons used on Geonsaugmented to or CaS. (bottom) but still has some thickness on cylinders with a hole in cross object from one side (top) sides. The last row has cylinders that are totally open, without a base or a top. Also not scale invariance is shown on Figre 10. As this study was only about ment cylinders, on NDL that samealso is necessary will be processed. to do for Also remaining case geons. of result being not decomposable it passes to next element on NDL. As one of primitives used on HFP is plane, this An primitive iteration was ends added when to it reaches group of geons. end ofbut still NDLthis butis oneiteration of main stageproblems may ended of using or not. HFP, Thisusing depends planes, on this NSL, makesif results NSL is of not segmentation empty it means in plane that instead are new of volume segments as it should to be processed. be, meaning So, that it appends geons alllike elements cube does on notndl, work on remove this approach. m fromthus, NSL a good andpath restarts to follow a newin future is to use anor hierarchical technique instead of iteration by vising again first element on NDL. HFP and make a deeper study of se thresholds. The iteration stage and entire algorithm ends when it has reached end of NDL and NSL is empty, meaning that re are no more segments to be decomposed. So, approach ends by returning entire collection of decomposed objects. Cylinder 1 Cylinder 2 Cylinder Geons-augmented CaS Decomposer During execution of manual segmentation test using HFP, one of complains of users was that some objects were over segment. This happens because it was Cylinder 4 Cylinder 5 Cylinder 6 Cylinder 7 Cylinder 8 used HFP approach. After executing adapted CaS approach with different similarity and similar count thresholds we notice that this problem still happens on this approach, so, to overcome this limitation it was introduced a new feature. The introduction of geons to verify if an object is decomposable or not. Cylinder 9 Cylinder 10 Cylinder 11 Cylinder 12 The geons are simple 3D objects, like cylinders, cones, cubes. The ory proposed by Biederman on [Biederman 87] called Recognition by Components states Figure that, 10: like SetEnglish of cylinders words that usedare toconstituted stop fromby over a segmenting number of phonetics, complex objects can also be composed by se simpler 3D objects, that is, by segmenting 4. EXPERIMENTAL EVALUATION complex objects we get se simpler objects. Thus we After completing approach implementation, it was necessaryato setverify of geons, efficiency partially depicted and effectiveness in Figureof7, to im- algo- added prove rithmdecomposition and refine results approach. according So, several to human tests were perception. exe- Since CaS approach uses HFP that uses primitives to calculate cost of merging clusters and re are some of geons that are same as se primitives, using