# Floor Plan Exploration Framework Based on Similarity Distances

Chia-Ying Shih1 and Chi-Han Peng10000-0002-6823-8029
National Yang Ming Chiao Tung University1

###### Abstract

Computational methods to compute similarities between floor plans can help
architects explore floor plans in large datasets to avoid duplication of
designs and to search for existing plans that satisfy their needs. Recently,
LayoutGMN [PLF∗21] delivered state-of-the-art performance for computing
similarity scores between floor plans. However, the high computational costs
of LayoutGMN make it unsuitable for the aforementioned applications. In this
paper, we significantly reduced the times needed to query results computed by
LayoutGMN by projecting the floor plans into a common low-dimensional (e.g.,
three) data space. The projection is done by optimizing for coordinates of
floor plans with Euclidean distances mimicking their similarity scores
originally calculated by LayoutGMN. Quantitative and qualitative evaluations
show that our results match the distributions of the original LayoutGMN
similarity scores. User study shows that our similarity results largely match
human expectations.

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[100]Computing methodologies Modeling methodologies

##  1 Introduction

To search for similar floor plan designs to copy or to avoid, architectural
designers often spend a lot of time exploring floor plans in massive datasets
such as RPLAN ([WFT∗19]). However, most floor plan similarity calculation
methods (including traditional methods such as Intersection-over-Union (IoU)
and neural network-based methods such as LayoutGMN [PLF∗21]) are not fast
enough to support searching in interactive speeds. Therefore, we propose an
efficient approach for the goal. In short, we project floor plans into a
common low-dimensionality data space such that their Euclidean distances would
mimic the similarity scores computed by LayoutGMN, a state-of-the-art floor
plan similarity calculation method. In this data space, data exploration tasks
such as: 1) searching for similar floor plans, 2) clustering, and 3) pruning
of nearly redundant designs, can be efficiently conducted. For example, our
method reduced the computation time for task 1) from 296.8 seconds by the
original LayoutGMN to just 8.7 seconds. To verify if the similarity measures
computed by our method match human expectations, we conducted user studies in
questionnaire formats. The results showed that the respondents largely agree
with our method’s similarity estimations.

Related Work. Determining the similarity between floor plans is a non-trivial
task because not only the shapes but also the connectivity of rooms need to be
considered. Such "distance" measures between floor plans is a key component
for generative methods [NCC∗20]. Early approaches only search for specific
areas (such as bedroom and living room) [KF05]. Recent methods tend to learn
the overall spatial features [SGCM17] and to present floor plans as planar
graphs encoding the rooms as vertices [PLF∗21]. Recently, LayoutGMN [PLF∗21]
produced state-of-the-art quantitative and qualitative performances of
similarity computation between floor plans by encoding room characteristics
(e.g., aspect ratios and locations) and room relationship (e.g., the relative
positions and overlapping areas) using an attension-based graph matching
network. However, LayoutGMN only computed tripled similarities in which each
floor plan don’t have a unique feature vector. This means that we cannot
simply project the floor plans to a common data space using the feature
vectors as coordinates. Another shortcoming of LayoutGMN is that the
similarity scores are not upper-bounded, further complicating the data
projection task.

Figure 1: Overview of our method. (b) Original pair-wise similarity scores
between floor plans are computed by LayoutGMN. (c) The floor plans are
projected to a common low-dimensional space such that the Euclidean distances
mimic the similarity scores, making data exploration tasks such as clustering
(d) easier to perform.

##  2 Method

Our method is summarized in Figure 1. We denote floor plans as $FP_{i}$,
$0\leq i<N$, $N$ is the number of floor plans in the dataset. Recall that
LayoutGMN compute similarity between floor plans by computing features vectors
(1024 in length) of triples of floor plans and then computing Euclidean
distances of the feature vectors as the similarity scores. Note that the
feature vector of a floor plan could be different when it is included in
different triples. Therefore, they could not be directly used as coordinates
in a common 1024-dimensional space. Through experiments, we have found that
directly applying traditional dimensionality-reduction techniques such as PCA
produced bad results because LayoutGMN tends to produce similarity scores of
very large value ranges. Therefore, we instead use cosine similarity to encode
distances between two floor plans into the 0 to 1 range as follows:

$Dist(FP_{i},FP_{j})=\frac{V_{i,(i,j,k)}\cdot V_{j,(i,j,k)}}{\lVert
V_{i,(i,j,k)}\rVert*\lVert V_{j,(i,j,k)}\rVert}*-1+1$ (1)

where $V_{i,(i,j,k)}\in R^{1024}$ is the feature vector of floor plan $FP_{i}$
when calculated among a triple of floor plans $FP_{i}$, $FP_{j}$, and $FP_{k}$
by LayoutGMN. Note that LayoutGMN selects the triples such that each triple
would include one "anchor" floor plan, one "positive" floor plan that has a
higher IoU score to the anchor, and one "negative" one that has a lower IoU
score to the anchor, respectively. The similarity score of two floor plans is
guaranteed to be the same even if the pair is included in different triples
because the pair is still processed by the same GMN module.

Next, we solve for the coordinates of the floor plans in a common data space
as a linear least squares optimization problem formulated as follows:

$\displaystyle\underset{X_{i},\ 0\leq i<N}{\text{argmin}}$
$\displaystyle\sum_{\forall
Dist(FP_{i},FP_{j})\,exists}{(\lVert(X_{i}-X_{j})\rVert-
Dist(FP_{i},FP_{j}))^{2}}$ (2)

where $X_{i}$ is the coordinate of $FP_{i}$.

##  3 Results and Applications

We tested on a computer with Intel i9-10900 2.80GHz CPU and 32GB Rams. We
trained LayoutGMN on the whole RPLAN dataset (77664 floor plans) to get
12492731 pairs of similarity scores, and used Google Ceres solver to solve the
projected coordinates of the floor plans. We can solve up to 3D data spaces
due to memory constraints. Quantitatively speaking, the solving using cosine
similarity (which took 56.65 minutes to converge) reduced the residuals from
1.9e+06 (random) to 1.3e+03, hinting a successful convergence. In comparisons,
the solving could not converge successfully using original Euclidean distances
or log distances. To qualitatively evaluate the projection results, in Figure
2, we show iterations of intermediate solutions of projected coordinates. By
coloring the data points with clustering of the similarity scores calculated
by LayoutGMN, we find that our projected coordinates largely match the
distributions of the original similarity scores.

Figure 2: Projected 3D coordinates of floor plans and their clustering
according to the original LayoutGMN similarity scores.

Applications. Our method enabled searching for similar and dissimilar floor
plans of a given floor plan in interactive speeds. With our method,
exhaustively comparing a floor plan to all others in the dataset took about
8.9 seconds, while using LayoutGMN to compute all the similarity scores took
about 296.8 seconds. Users can also insert new floor plans into the dataset.
To calculate the coordinate of the new data point, we use LayoutGMN to
calculate its similarity scores to all existing floor plans in the dataset,
and solve the optimization (Equation 2) again but with all existing data
points’ coordinates fixed. Figure 3 shows multiple results with existing floor
plans in the dataset and novel designs by users as inputs. In general, we
found that it is easier to find designs similar to existing entries in the
dataset rather than novel designs specified by the user. We think the reason
is due to the limited diversity of the dataset. Finally, our method enabled us
to detect and prune nearly redundant entries in the original RPLAN dataset. We
found 4419 redundant floor plans that are only 50 pixels or less different to
others (layout images are of a 256x256 resolution).

Figure 3: Searching similar designs by existing (left) or user-defined (right)
floor plans.

User Study. We conducted a questionnaire-based survey of 25 correspondents.
Our questionnaire is divided into two parts: ranking and judgment. By
calculating the rank correlation, our system obtained a positive correlation
result of 63.6% in the ranking part. In the judgment section, there is an 85%
pass rate.

##  4 Conclusion

We propose a method to encode the similarity measurements of LayoutGMN in a
common low-dimensional space to facilitate much more efficient exploration.
For future work, we would like to explore different ways to encode the
similarity scores such as weighted sums of Euclidean distances and cosine
similarity.

## References

  * [KF05] Kiyota K., Fujiyoshi K.:  Simulated annealing search through general structure floor plans using sequence-pair.  _Electronics and Communications in Japan (Part III: Fundamental Electronic Science) 88_ , 6 (2005), 28–38.
  * [NCC∗20] Nauata N., Chang K.-H., Cheng C.-Y., Mori G., Furukawa Y.:  House-gan: Relational generative adversarial networks for graph-constrained house layout generation.  In _European Conference on Computer Vision_ (2020), Springer, pp. 162–177.
  * [PLF∗21] Patil A. G., Li M., Fisher M., Savva M., Zhang H.:  Layoutgmn: Neural graph matching for structural layout similarity.  In _Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition_ (2021), pp. 11048–11057.
  * [SGCM17] Sharma D., Gupta N., Chattopadhyay C., Mehta S.:  Daniel: A deep architecture for automatic analysis and retrieval of building floor plans.  In _14th IAPR International Conference on Document Analysis and Recognition (ICDAR)_ (2017).
  * [WFT∗19] Wu W., Fu X.-M., Tang R., Wang Y., Qi Y.-H., Liu L.:  Data-driven interior plan generation for residential buildings.  _ACM Transactions on Graphics (TOG) 38_ , 6 (2019), 1–12.