1 Introduction
Large scale virtual environments are an important feature across a plethora of applications such as massivelymultiplayeronline computer games, movies, and even simulators used to train selfdriving cars. Manual authoring of environments at these scales is impractical and there is a need for algorithms that can automatically generate realistic virtual environments. To be considered useful, it is important that automatic algorithms are able to accommodate constraints stipulated by domain experts. In this paper, we address the problem of automatically generating furniture layouts for indoor scenes. We propose a simple algorithm to automatically populate empty rooms with realistic arrangements of 3D models of furniture and other objects, using occurrence and placement statistics learned from a training database of layouts of CAD models. Our method supports a wide variety of a priori constraints. It can be used in conjunction with methods such as [MSK10, MVLS14] that place rooms within buildings, to automatically generate complete indoor virtual environments.
The computer graphics literature is rich with methods that enable 3D content creation, from landscapes [CGG17] and urban sprawls [PM01] to individual objects such as furniture [LXC17], buildings [MWH06, NGDA16], etc. These methods involve varying degrees of userinteraction to achieve realism and/or aesthetic appeal. Procedural approaches rely on parametric controllability while methods that are posed as optimization rely on constraintdriven controllability. A third class of methods adopts a datadriven approach to generate or edit models based on features learned from training examples [FKS04, EVC15, LXC17].
We propose a new datadriven, probabilistic, generative model for 3D room layouts (Sec. 2). Our model learns statistics from a database [SYZ17] containing over rooms designed by humans (Sec. 3). We categorize over 3D models from the database and learn conditional statistics across these categories. The output space of this learned model is a highdimensional combination of discrete and continuous variables. Our model is based on directed, acyclic dependencies between categories, which allows easy and very efficient ancestral sampling. Each sample results in a furniture layout. We demonstrate the flexibility of this approach by incorporating userspecified constraints such as accessibility, sizes and shapes of rooms, locations of doors and windows, and constraints on the location of furniture items such as sofas and television screens (Sec. 4). Finally, we present a user study showing that layouts generated by our model are realistic (equal quality to those in the training set), and compare favorably to the stateoftheart method [WSCR18] (Sec. 5).
1.1 Related work
[1]  [2]  [3]  [4]  [5]  [6]  [7]  ours  

room type  ✓  ✓    ✓  ✓      ✓ 
room size  ✓  ✓  ✓  ✓  ✓  ✓  ✓  ✓ 
room shape  ✓              ✓ 
traversability            ✓  ✓  ✓ 
object existence      ✓      ✓  ✓  ✓ 
object placement              ✓  ✓ 
fully automatic  ✓  ✓    ✓  ✓      ✓ 
Priors for understanding structure in indoor scenes
: Choi et al choi13cvpr performed 3D object detection and layout estimation by inferring spatial relations between objects using a discriminative, energybased formulation. They do not present a generative model over layouts. Zhao and Zhu zhao11nips,zhao13cvpr built a probabilistic grammar model, using specifically engineered production rules, over cubebased 3D structures constituting parts of rooms. This grammar generates arrangements of coarse blocks and does not result in layouts of entire rooms. Similarly, treating objects as cuboids, Del Pero et al delpero12cvpr proposed a generative model over room size and layout using learned distributions for the dimensions of the cuboids. The model does not learn interobject relationships such as cooccurrence or relative locations. Although the importance of such relationships was discussed in followup work
[DPBF13], interobject relationships were not incorporated in the generative model.Generating realistic furniture layouts: A common approach is to adopt an energybased formulation [MSL11, YYT11, SKLTZ16, HPSC16, QZH18] with potentials between objects to impose constraints and preferences. The method of Handa et al handa16icra generates room layouts by optimizing a pairwise energy term using simulated annealing, with random initialization. Sadeghipour Kermani et al sadeghipourkermani:2016:learnsynth propose a method for generating bedrooms, that separates the sampling of classes and counts from the spatial arrangement. Liang et al Liang:17 also propose a twostep method, demonstrated on five room types. Objects are first selected based on statistics learned from a database, without considering interobject relationships. Their locations are then chosen by MCMC sampling from a pairwise energy model. None of these methods reason about smaller objects positioned on the furniture, nor objects mounted on the walls or ceiling. Moreover, both simulated annealing and MCMC are slow, and not guaranteed to converge to a valid layout.
Very recently, Qi et al qi18cvpr represent indoor scenes using a probabilistic grammar, using a conditional Gibbs distribution as prior on its parse graphs. The conditioning parameter is learned from a large database. Their approach requires considerable manual modeling including specification of potential functions and grouping relations between objects such as chairs and tables. Novel layouts are generated using MCMC sampling, along with simulated annealing; this takes around 2400s per layout. Wang et al wang18tog exploit the power of convolutional neural networks (CNNs). Their method generates layouts by using three different CNNs to decide whether to add furniture, what furniture to add, and where to place it. This approach avoids a costly MCMC optimization process, but still takes several minutes on a GPU to sample a single room, and several days to train the models. Both these approaches are trained with the same dataset that we use in this paper. While they are fully automatic, neither supports inputing userspecified constraints.
Other methods suggest new layouts based on partial input, such as the object classes and an initial arrangement [MSL11, YYT11, FCW17]. Fu et al Fu:2017 exploit knowledge of how human agents interact with indoor environments to synthesize entire room layouts from a room shape and a few classes of objects that are to be present. This method is the fastest among prior works, taking approximately 2s to generate a layout.
Finally, some works model small areas of rooms centered around one item of furniture, instead of complete layouts. Fisher et al fisher12siggraph propose a method that learns from a dataset of 130 layouts, to embellish parts of rooms by adding relevant objects around (e.g. chairs around a table) as well as on (e.g. books on a table) furniture. It does not model entire layouts of rooms containing complex arrangements of furniture. Ma et al ma16tog again generate small areas of rooms by embellishing a focal object, but they decide the classes and locations of objects to add by reasoning over human actions that could take place in the scene.
Summary and motivation: Although many algorithms have been proposed to generate furniture layouts, none of them is fully automatic, considers interobject relationships, and is amenable to a diverse range of userspecified constraints (Table 1). Most automatic methods are limited to simple constraints such as room type, shape, size and the presence of a particular object. While other constraints could be applied by rejection sampling, this is prohibitively expensive, as these models are at best
slower than ours to sample from, and even slower for methods requiring no user interaction. Adding constraints to energybased models is possible by introducing new potentials, but this requires careful design and engineering. Moreover, it would make sampling even more costly. Thus, it is not practical to incorporate complex constraints in any previous approaches to layout generation.
1.2 Contributions
We make the following contributions:

We propose a generative model for room layouts, based on a directed graphical model that captures highorder relationships between objects;

Our generative model enables efficient, ancestral sampling of objects and their attributes; and

Our method is fully automatic and allows specification of general a priori constraints using rejection sampling.
2 Automatic generation of room layouts
We begin by sampling a room type (e.g. kitchen, living room), then sequentially sample furniture instances, conditioned on the room type and instances already sampled. We partition rooms into cells and sample objects and their positions within these cells (Fig. 2) such that geometric intersections will not occur. We begin with furniture objects (Sec. 2.2), which define the structure of the room. Then, in an embellishment step (Sec. 2.3), we sample instances of other categories, given the furniture items and their locations. The overall sampling process is illustrated in Fig. 1.
The parameters used for sampling instances of objects, for cell assignments and positioning within a cell are learned from the dataset (Sec. 3
). These are simple parametric models, which are humaninterpretable and modifiable.
2.1 Classes and categorization
The dataset contains CAD models, where each model is assigned an object class such as “television”, “bathtub”, “armchair”, etc. There is a total of 2500 CAD models and 170 object classes in the collection. We introduce an additional set of labels called categories: furniture, small objects such as books and laptops, wall objects such as picture frames, and ceiling objects such as lamps. We manually specified a second mapping from models to categories (Fig. 3). Our sampling strategy for models differs between the different categories, as discussed in the next sections.
2.2 Sampling furniture
We place furniture instances by sampling counts of singletons (i.e. individual objects), and of motifs and abutments, which are spatiallyrelated groups learned from the training data. For each instance, we sample a cell it is to be placed in (e.g. ‘against the east wall’), and its orientation and padding. After all furniture counts and instance parameters have been sampled, we position the resulting objects deterministically. The room structure is finalized when cells (and hence the room) are sized to accommodate the objects and their paddings.
Singletons: We sample singletons using algorithm 1, where functions SampleNumInstances, SampleCell, SampleOrientation and SamplePadding sample from distributions whose parameters are learned from training data. The arguments to these functions signify what the underlying distributions are conditional on. At each iteration (line 6 of algorithm 1), cells expand to fit the sampled objects, ensuring no intersections between objects.
Motifs: Motifs are groups of items that are present together in many examples of the dataset, such as a table with chairs around it. We sample counts and instance parameters for each motif following lines 5–10 of algorithm 1, but in this case represents a motif rather than a singleton CAD model. Then, we set the relative offsets and orientations between items within a motif as observed in a randomly selected instance of the motif in the training database. This nonparametric strategy for determining relative placement yields coherent, visuallypleasing groups of furniture, and eliminates the need for expensive collision/intersection tests between meshes.
Abutments: Abutments are groups of items that appear in rows, abutting one another, with variations in their sequence, e.g. a row of cabinets in a kitchen along with a dishwasher, refrigerator and/or washing machine. Again, we sample counts and instance parameters for each abutment using lines 5–10 of algorithm 1, where
now represents a class of abutment. The furniture items within an abutment are modeled as a Markov chain with a terminal state; for each instance of the abutment, we sample from this Markov chain to obtain a specific sequence and number of CAD models. The transition probabilities of the Markov chains are learned during training.
2.3 Embellishment
Ceiling objects: Given a room type , we draw a single CAD model randomly according to a discrete probability mass function (pmf) over models in this category. The number of instances of is determined using . This number is rounded up so that it can be factorized into a product of integers and the objects are positioned on a grid.
Wall objects: For each CAD model that is a wall object, we determine the number of instances in similar fashion to furniture in lines 2–5 of algorithm 1
. Each instance is then assigned to a wall uniformly randomly and its position on the wall is a combination of a Normal distribution along the
axis and Uniform distributions in
and . The parameters of the Normal distribution are learned (conditioned on ). If this results in a geometric conflict (intersection with other wall objects, doors, etc.) we reject the sampled location and repeat the process until there are no conflicts.Small objects: For each furniture instance with CAD model , we sample small objects nonparametrically conditioned on and . We choose a random instance of in a room of type from the database, and replicate the configuration of small objects associated with that instance.
2.4 Algorithm summary
To summarize, we first randomly sample the type of room from a discrete distribution over 9 room types found in the database. The distribution (pmf) of is learned during training. Then, we sample furniture items conditioned on : first singletons, then motifs and finally abutments. The numbers and instances of each item are determined by parameters learned during training. Once all furniture items are sampled, and assigned to cells, we use a deterministic placement algorithm that calculates their final positions in the room. Then, we sample ceiling objects and wall objects conditioned on and the furniture placed. Finally, we sample small objects conditional on the furniture in the room and .
3 Training
Dataset: We use a large dataset of groundtruth room layouts to learn parameters that are then used for automatically generating layouts. SUNCG [SYZ17] is a new dataset of 45000 apartment layouts, created by humans, and separately verified as reasonable by humans. Each apartment has an average of 8.1 rooms; the majority are annotated with the room type. The apartments are designed with an online tool, and contain objects of 170 classes, represented by around 2500 CAD models. There are 4.5M object instances; each consists of a reference to a CAD model, and its location and orientation in the room.
Number of instances: We model the number of instances of each CAD model as being conditional on the model , the room type , and on the number of furniture instances already sampled for the class . The distribution (pmf) over count bins is calculated as a histogram (normalized) over all scenes in the database of type
. Further, a Poisson distribution is fitted to the observed
in all scenes with . SampleNumInstances (line 5 of algorithm 1) is implemented in two steps. First, we draw an indicator variable according to . If this variable is less than or equal to 4, then we return it as the number of instances. Otherwise, we return a sample from the Poisson distribution.Instance attributes: For each model , during training, we calculate a pmf over 9 cells (4 corners, 4 edges and internal) by normalizing the histogram of occurrences. We implement SampleCell (line 7 of algorithm 1) by returning a cell according to this pmf. For models in internal cells, we count the number occurrences where they are aligned (positively or negatively) with respect to any axis and the number of “nonaligned” instances, and use this to learn a pmf. We implement SampleOrientation (line 8 of algorithm 1) by sampling an indicator variable according to the pmf for orientations. If this variable indicates nonalignment, we sample an orientation uniformly at random. Finally, we model padding around CAD models as a 4D diagonalcovariance Normal distribution conditioned on the CAD model . The dimensions correspond to padding on each side of the object: infrontof, behind, totheleftof and totherightof. SamplePadding (line 9 of algorithm 1) returns a sample from this 4D Normal distribution. The knowledge learnt during training is interpretable; Fig. 11b,c show values from the pmfs, indicating typical placements of objects, while Fig. 11a shows typical locations where we place various classes. In both cases, these agree well with human intuition on interior design.
Motif discovery: We search the training set for all joint occurrences of a given tuple of classes (e.g. table, chair, chair) within a room. For every occurrence of one of these classes – designated as the base object – we calculate displacements of the centres of the other objects relative to the base object. We model these displacements as points in a dimensional space and cluster them with a Dirichlet process mixture model (DPMM) [Ras00], fitted by variational inference. We use Gaussian clusters with diagonal covariance and fit a DPMM per tuple of classes. We calculate the area inside the contour for the location of each element in the motif; if all of these are less than a threshold, then the cluster is accepted as a motif. We store the CAD models, relative locations, and orientations for every occurrence assigned to the cluster; one of these will be selected when instantiating the pattern. Some examples of motifs we discover are given in Fig. 4.
Abutment discovery: We discover abutments in two stages. First, we gather sets of sequences of CAD models, where each set will ultimately become an abutment pattern. Each sequence of CAD models represents an abutting series of instances in the training set. Then, for each , we calculate the transition probabilities for the corresponding Markov chain, as maximumlikelihood estimates given the CAD model sequences . More precisely, we collect such sets in a collection , initialising to be empty. While doing so, we maintain the invariant that , and do not contain any sequences that share CAD models. For each room in the training set, we find all pairs of objects that abut, based on their rotated boundingboxes touching at an edge. These pairs are combined transitively to form full sequences of objects , each being a row of abutting objects of some orientation. For each objectsequence , ignoring those with just two objects, we check if any of its CAD models appears in any sequence in a set already created. If so, we add the objectsequence to ; if not, we create a new one storing just , and add it to . In the first case, we also check that adding the sequence to has not broken the invariant that sets do not share CAD models; if it has, we merge sets until the invariant holds again. At the end of the above process, each contains many sequences of CAD models, each of which we will treat as a sample from the Markov chain . It is then straightforward to learn the transition probabilities for by maximising the likelihood of all the sequences . Some examples of abutments we discover are given in Fig. 5.
4 Constraints
Our generative model accommodates diverse constraints using rejection sampling as a general mechanism, i.e. we sample layouts until we obtain one that satisfies all constraints. We demonstrate the versatility of our generative model using some example constraints. Incorporating other constraints can be achieved similarly as long as a given layout can be verified to satisfy them. Since our sampling process is very fast (tens of milliseconds per room), any inefficiency due to rejection sampling is outweighed by its ability to serve as a common mechanism to impose a wide range of constraints (Tab. 2). In some special cases, we can avoid rejection sampling by allowing users to explicitly manipulate parameters of distributions learned (Fig. 9).
Room type and size: As the room type has no ancestors in our model, it can directly be assigned a constrained value, avoiding rejection sampling entirely. Since room size is a continuous value, and the probability of any sample satisfying this is zero, we allow a small tolerance on each dimension (2% in all our examples).
Traversability: A layout is traversable if there exists a path between all points in free space (regions with no furniture) and from all points in free space to all doors in the room. To verify this, we first rasterise an orthographic projection of the furniture onto the floor plane at a fixed resolution and identify free space as the complement of this footprint. We calculate (areas where people can stand or pass) via morphological erosion of the free space using a circular kernel of radius 0.25m and also add regions on doors to . Similarly we calculate regions that require access using morphological erosion, but with a larger kernel. Then we verify traversability by checking whether is reachable from via some .
Gap placement and clearance: Ensuring there is a gap at a particular location allows users to augment layouts with their own 3D models, that are not part of our system. In order to make rejection sampling efficient, rather than just discarding layouts until one that satisfies the constraint is found, we directly place a ‘gap instance’ in a suitable cell, ensuring that no object will occupy the relevant space. Note that some rejections will still occur, as cell locations are not known precisely until all furniture items are placed. We also allow users to specify the clearance around particular objects, regardless of where in the room they are placed, e.g. to allow additional space next to a bed that must be used by a mobilityimpaired individual. This is implemented efficiently by directly adjusting the parameters of the relevant padding distribution.
Object placement: We allow users to place instances of CAD models known to our system, at specific locations – e.g. a bed against a particular wall. Similarly to placing gaps, we ensure that a suitable instance is placed in the relevant cell, thereby greatly reducing the chances of rejection.
Doors, windows and refurnishing: We model door and window specification using a combination of gapplacement, at edges of rooms, and traversability (the relevant area is included in ). This allows us to support refurnishing existing rooms from SUNCG – that is, generating new furniture, while retaining the existing size/shape, doors, and windows. This is valuable for generating complete, realistic rooms without any user input.
5 Results
In this section, we present qualitative results to highlight the samples (with and without constraints) generated using our model, and quantitative results measuring performance. We also assess the quality of our generated layouts via a simple user study. All rendered images were obtained using pathtracing [Jak10]. The execution times reported in this paper were obtained using our unoptimized and sequential Python implementation, on an Intel Xeon E52620v3 processor, using less than 1GB of RAM.
5.1 Generating layouts
Unconstrained output: In Figure 6, we show some output examples from our generative model, without any constraints specified. Our model produce results without objects intersecting and mimics the diversity found in the training dataset – both in terms of the types of rooms as well as the objects in them. The cooccurrence and relative placements of objects are also realistic and natural. Unconstrained layout samples are generated in 0.04s on average.
Examples with constraints: Figure 7 shows examples of layouts where the room size and placement of one object was specified by the user. Note that the other sampled objects in the room are automatically chosen, and placed harmoniously. For example, in the first image, the constraint was “place a bed near the top right corner”. Our method automatically places nightstands on either side of the bed.
Figure 8 shows sample layouts where the shapes of the rooms and the locations of doors where specified as constraints. Note that the doors are unobstructed in the generated layouts.
Figure 9 shows examples of layouts where a user has specified particular clearances to be respected around specific object classes. The bar plots on the first column (solid blue) show the ranges of clearances learned during training on the left (L), front (F), right (R) and back (B) of the models sampled from four chosen classes (sofa, double bed, sink and bath). The pink squares on the bar plots depict user modifications of the learned parameter (dashed blue rectangles). For each specified constraint (rows), four sample outputs are visualized (columns), and the impact of the user specification is shown using pink arrows. In this particular example, the constraints are imposed by directly editing learned parameters rather than using rejection sampling, which leads to faster runtime.
Constraints producing uncharacteristic layouts: One benefit of training a constrainable generative model is that we can generate rooms fulfilling constraints that are never fulfilled in the training dataset, or only very rarely. We demonstrate this by using random sets of reasonable constraints and identifying those sets of constraints which are not jointly satisfied by any room in the SUNCG dataset. Then, we use our model to sample a room that does satisfy the constraints. Examples are given in Fig. 10.
Runtime with constraints: Table 2 shows the impact of applying different constraints on the running time of our method. Our singlethreaded Python implementation takes just 0.04s to sample an unconstrained room layout. Even with complex constraints applied, the sampling time remains practical.
Constraint  Time per sample /s 

unconstrained  0.04 
room type  0.04 
object class exclusion  0.04 
clearance  0.04 
traversability  0.05 
object placement  1.4 
gap placement  1.8 
room size  6.8 
size + doors + windows  112 
5.2 User study
We assessed the realism of layouts generated using our model via a user study comparing its output to humandesigned rooms from the SUNCG database. We presented 1400 pairs of images to eight nonexpert users and asked them to identify the image with a more realistic, or natural, layout of objects. In each case, one image was a groundtruth (humandesigned) layout from SUNCG, and the other was a sample from our model; the order of the two images was randomised for each pair. The goal here is that our samples are indistinguishable from humandesigned layouts, i.e. of equal perceived quality to them, so users prefer ours 50% of the time.


Percentage of imagepairs where users preferred (i.e. deemed more realistic) a layout sampled from our model, as opposed to a groundtruth layout from SUNCG (‘Ours pref.’). Higher is better, with 50% indicating that our samples are indistinguishable from groundtruth. Ranges are the 95% confidence interval
[ET86]. (a) Unconstrained layouts; (b) Constrained layouts.Unconstrained: We sampled several hundred random layouts from our model without constraints, and a similar number of groundtruth layouts from SUNCG. We presented images in the form of either overhead renderings or firstperson camera views from inside the room. The observed user preferences are given in Table 2(a); we see that our layouts are equivalent in perceived quality to the humandesigned layouts in the training set. Specifically, in firstperson views, users slightly preferred our layouts; in overhead views, our layouts are indistinguishable from groundtruth up to statistical significance.
Constrained: We assessed room layouts generated by our model with constraints as we did layouts without constraints, but using only overhead renderings. We considered two representative settings for constrained generation: (i) fixing the room size and placement of one object; and (ii) fixing the room size and locations of doors and windows (implying gap placement and traversability constraints). In both cases, we generated several hundred random examples. For (i), we randomly generated arbitrary, but meaningful, pairs of constraints and sampled one layout fulfilling each. For (ii), we randomly selected rooms from SUNCG, and used their size and door/window locations as constraints for our model, again sampling one layout for each. In the second case, our model refurnishes existing rooms. In both cases, we compare our samples against arbitrary groundtruth rooms, which typically do not fulfill the same constraints, i.e. we test the realism of our samples and not whether constraints are fulfilled (which is guaranteed by rejection). Results are given in Table 2(b). With room size and the placement of one object constrained, our layouts are indistinguishable from ground truth up to statistical significance. With room size and the positions of doors constrained, users preferred humandesigned layouts.
Room type  Ours pref. 

bedroom  
living room 
Comparison with [WSCR18]: We compared randomly generated unconstrained samples from our model with those generated by the stateoftheart CNNbased method of [WSCR18]. We presented users with 550 pairs of images, each showing one layout generated by our method and one by that of [WSCR18]. We restricted the room types to those supported by both our method and theirs, i.e. bedroom and living room. The users were again asked to identify the image with a more realistic arrangement of objects. Results from this experiment are shown in Table 4. We see that our layouts are often preferred to those of [WSCR18]. Moreover, our model is interpretable and fast to train, whereas theirs is a noninterpretable blackbox model trained over several days.
6 Discussion
Comparison with prior works: Probabilistic generative methods for room layouts are challenging to sample from. Often the sampling is not guaranteed to converge to a valid layout, espcially when many objects are present. e.g. the model proposed by Handa et al handa16icra. This particular model also requires that the number of objects, and size of the room, be specified manually. Our model performs favorably compared with with the very recent work [WSCR18] that learns millions of parameters over days of training. For over 70% of pairs presented, users preferred our layouts to theirs. In addition to accommodating constraints easily, our model has another advantage in that the parameters learned are over semantically meaningful concepts (categories such as furniture) allowing direct modulation of learned parameters as shown in Figure 9. Although we manually specified padding constraints, they could be calculated from alternatives such as humancentric affordances [QZH18].
Interobject relationships: We explicitly discover and encode relationships across classes of objects using patterns such as motifs and abutments. These patterns capture higher order relationships (not just pairwise); in the case of abutments, they are able to model sequences of variable lengths which may not be present in the training database. Figure 12 shows unnatural layouts generated when interobject relationships due to motifs and abutments are not modeled. Additionally, implicit relationships are captured between different CAD models of the same class in a given layout, through the conditioning on the number of objects already placed (line 5 of algorithm 1). For example, the generative process may not favor a large item from a class if multiple small items from that class have already been sampled.
Novelty of samples: Large generative models run the risk of overfitting their training set, memorizing the training data instead of generalizing to produce novel samples. Fig. 10 shows that our model is able to generate constrained layouts even when the constraints are not fulfilled by any room in the training set. Thus, it is not simply memorizing the training data, but is creating new arrangements. As a second demonstration of this, we directly searched for the most similar layouts in the training set, to layouts generated by our model. The retrieved layouts are typically quite different from our samples in arrangement and exact object counts, which confirms that our model is generalizing.




(a)  (b)  (c) 
Efficient implementation of constraints: For many of the constraints listed in Section 4, rejection sampling can be avoided using alternative implementations. For example, space constraints may be tailored at the class level by biasing the 4D Normal distribution learned for padding. Figure 9 shows direct editability of learned parameters. Example layouts produced by the modified distribution are shown on the right, along with the effects of the user manipulation on the corresponding objects. Another example of a constraint that may be implemented efficiently is the specification of certain object classes (or CAD models) as not desirable. Rather than relying on rejection sampling, these classes (or models) may be preemptively avoided during instantiation.
Interpretability: Since our model learns parameters associated with semantically meaningful categories and positions, the learned results can be interpreted and manipulated. Figure 11a visualizes heatmaps of where the model places a few chosen object classes. For each class, we sampled 2500 rooms, and plotted (black dots) where objects of the indicated class were placed (normalizing the room bounds to a unit square). The model has learnt to place different classes meaningfully – for example, showers are almost always at the corner of a bathroom, dining tables are often at the center of a room, and toilets are always against a wall. Figure 11b and Figure 11c list the highest and lowest probability entries for object positioning and orientation. We obtained these numbers by averaging over the corresponding probabilities for all CAD models in the stated classes. The numbers align with our expectation that chairs and tripods are not typically placed along the edges of rooms, and that they are less likely to be aligned with the walls than beds, kitchen cabinets or dishwashers.
Room shape: In our implementation we decompose nonrectangular rooms into rectangular regions and apply our cell structure on each region. Other strategies to partition rooms into cells may be adopted as long as they are kept consistent across training and sample generation. However, the choice of partitioning strategy may impact the quality of results.
Multiple, simultaneous constraints: Another advantage of rejection sampling as a general mechanism to impose constraints is that support for multiple constraints is trivial to implement. However this flexibility is accompanied by a penalty in terms of runtime. The time taken to generate a sample that satisfies multiple constraints, on average, is the product of the times taken to support each constraint.
Limitation: a posteriori editing: Our model is designed for fast generation of layouts with prespecified constraints but our formulation does not facilitate editing an existing (previously sampled) layout. While we can handle a priori specification such as “I want a new layout such that this television set is placed against the east wall”, it cannot handle a posteriori editing such as “In the previously generated layout, move the television to the east wall”.
7 Conclusion
We have presented an efficient, probabilistic, datadriven, generative model for indoor furniture layouts. The algorithm used to generate layouts is simple and the parameters learned from training data are humaninterpretable. We demonstrated that our model is able to accommodate a variety of constraints using rejection sampling as well as editing of learned parameters. We presented qualitative and quantitative results through rendered layouts, performance measurements and a user study. These showed that our layouts are realistic, and preferred by users over the stateoftheart method of [WSCR18].
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