Dark Reciprocal-Rank: Teacher-to-student Knowledge Transfer from
Self-localization Model to Graph-convolutional Neural Network
Takeda Koji
Abstract— In visual robot self-localization, graph-based scene
representation and matching have recently attracted research interest as robust and discriminative methods for selflocalization. Although effective, their computational and storage
costs do not scale well to large-size environments. To alleviate
this problem, we formulate self-localization as a graph classiﬁcation problem and attempt to use the graph convolutional
neural network (GCN) as a graph classiﬁcation engine. A
straightforward approach is to use visual feature descriptors
that are employed by state-of-the-art self-localization systems,
directly as graph node features. However, their superior
performance in the original self-localization system may notnecessarily be replicated in GCN-based self-localization. To
address this issue, we introduce a novel teacher-to-student
knowledge-transfer scheme based on rank matching, in which
the reciprocal-rank vector output by an off-the-shelf state-ofthe-art teacher self-localization model is used as the dark knowledge to transfer. Experiments indicate that the proposed graphconvolutional self-localization network (GCLN) can signiﬁcantly outperform state-of-the-art self-localization systems, aswell as the teacher classiﬁer. The code and dataset are available
at https://github.com/KojiTakeda00/Reciprocal rank KT GCN.

I. I NTRODUCTION
In visual robot self-localization, graph-based scene representation and matching have attracted recent research interestas robust and discriminative methods for self-localization.
For example, in [1], an image-based self-localization application was addressed by representing each view image
frame as a graph node and by connecting neighboring image
frames via graph edges. In [2], a subimage-based selflocalization application was addressed by representing semantically segmented regions as graph nodes and connecting
neighboring segments via graph edges. In these applications,a query scene graph is matched against each map graphaccording to the similarity of graph node descriptors (e.g.,
image descriptors [3], region descriptors [4]) and the graphstructure. Although they are effective, their computationaland storage costs increase in proportion to the environment
size and do not scale well to large environments.
To alleviate this problem, we formulate self-localization asa graph classiﬁcation task and use the graph convolutional
neural network (GCN) as a graph classiﬁcation engine.
Our approach, wherein the GCN is used as a scene graphclassiﬁer, is analogous to the recent paradigm of using a convolutional neural network (CNN) as a scene image classiﬁer
Our work has been supported in part by JSPS KAKENHI Grant-in-Aid
for Scientiﬁc Research (C) 17K00361, and (C) 20K12008.
K. Takeda is with Graduate School of Engineering, University of Fukui,Japan. K. Tanaka is with Faculty of Engineering, University of Fukui, Japan.

{takedakoji00, tanakakanji}@gmail.com

Tanaka Kanji

Fig. 1. We propose the use of the reciprocal-rank vector as the dark
knowledge to be transferred from a self-localization model (i.e., teacher) toa graph convolutional self-localization network (i.e., student), for improving
the self-localization performance.

[5]. We inherit desirable properties of the classiﬁcation task
formulation, such as the ﬂexibility in deﬁning place classes[6], compressed classiﬁer model [7], and high classiﬁcation
speed [8]. A key difference from the image classiﬁer tasks
is that the input visual data must be translated to graph data
before being input to the GCN. This problem is the main
focus of the present study.
A straightforward approach is to employ visual featuredescriptors used by state-of-the-art self-localization systems,
such as CNN-based [3], GAN-based [9], and autoencoderbased features [10], directly as graph node features. However,
the main concern is that visual feature descriptors are not
optimized for graph convolutions. In theory, their superior
performance in the original self-localization system may
not necessarily be replicated in GCN-based self-localization.
Our experimental results indicated that the self-localization
performance deteriorated when visual feature descriptors
were directly used as a graph node feature descriptor in the
GCN model.
To address this issue, we introduce a novel teacher-tostudent knowledge-transfer scheme based on rank matching[11] (Fig. 1), inspired by our previous studies [12]–[14]. The
basic idea is to introduce a state-of-the-art self-localization
model (e.g., bag-of-words image retrieval [15], object proposal and matching [4], and deep image feature descriptor[3]) as a teacher classiﬁer. This approach is inspired by therank-matching loss used by recent transfer-learning schemes[11], where rank values are employed as the dark knowledgetransferred from the teacher classiﬁer to the student classiﬁer.
While rank transfer has been used in transfer learning with
CNNs, its use in feature transfer with GCNs is non-trivial
and was addressed for the ﬁrst time in this study.

Fig. 3.
Fig. 2.

System architecture.

The main contributions of this work are summarized asfollows: (1) We propose a novel graph node descriptor,
which transfers the prediction of an off-the-shelf state-ofthe-art teacher self-localization model to the student GCN
classiﬁer. (2) We show that a class-speciﬁc reciprocal-rank
vector is a proper and effective representation of the dark
knowledge to transfer. (3) We experimentally show thatthe proposed graph-convolutional self-localization network(GCLN) can signiﬁcantly outperform state-of-the-art selflocalization systems, as well as the teacher classiﬁer. (4) Wemake the code and dataset publicly available1 .
II. R ELATED W ORK
Visual feature descriptors for visual robot self-localization
have been intensively studied. Recently, the use of intermediate features of deep neural networks (e.g., CNN [3], GAN[9], and autoencoders [10]) as discriminative and invariant
visual image descriptors has become common. Additionally,
the bag-of-words model has been used as a highly efﬁcient
image descriptor in state-of-the-art self-localization systems[15]. Moreover, it is straightforward to extend such an image
descriptor to a subimage descriptor by segmenting images
into subimages [4]. The effectiveness of image features has
also been shown in several graph-based place recognition
frameworks. In [16], the feature similarity between query anddatabase images is represented in graphs, and performanceis improved over a simple feature matching method by using
diffusion operation. On the other hand, in [17], performanceof SeqSLAM is improved by removing the assumption thatthe robot is moving at a constant speed, which is based on a
directed acyclic graph -based method. In [18], a covisibility
graph is used to encode the geometric information between
visual words, which is based on the graph kernel for graphmatching. However, the use of visual feature descriptors in
the GCN framework is not straightforward and has yet to beinvestigated.
The GCN was recently developed and is one of the mostpopular types of deep graph neural networks. The GCN
provides a ﬂexible and descriptive model and has beensuccessfully used in applications where the traditional CNN
proved to be either inefﬁcient or unsuitable (e.g., chemical
reactivity [19], web-scale image retrieval [20]). Recently, theGCN has also been used in robotics and vision applications,such as the representation and parsing of spatially sparsethree-dimensional (3D) point clouds [21]. Additionally, theuse of scene graph representation has recently attracted
1 https://github.com/KojiTakeda00/Reciprocal rank KT GCN

Single-view subimage-level scene graph (SVSL).

research interest. In [22], a new view-based GCN was proposed, in which 3D shapes are recognized according to thegraphical representation of multiple views. In [23], the worstcase graph matching method was proposed for addressing
the challenges caused by appearing and disappearing landmarks, in which the spatial similarity of the landmarks withthe worst appearance similarity is maximized. However, inthe present study, we revisit a classical visual robot selflocalization application with the aim of improving existing
solutions.
The problem of visual robot self-localization has beenstudied with regard to various aspects. Several studies havefocused on challenging self-localization scenarios, e.g., homogeneous orchard scenery [24], limited onboard resources[25], and highly dynamic environments [26]. Furthermore,advanced self-localization methodologies have been proposed, such as visual feature selection [27], hierarchical localization [28], quantifying the self-localization safety [29],key-frame selection [30], end-to-end self-localization [31],augmenting the scan context [32], sequence-based matching[33], geometric hashing [34], and persistence reasoning [35].
Additionally, the use of prior domain knowledge, e.g., OpenStreetMap [36] and Google Earth [37], has become common.
In our previous studies, the ranking-based scene descriptors
were explored in the context of image change detection[12], knowledge distillation [13], as well as rank fusion[14]. However, our approach focuses on the fundamental
problem of scene modeling, which is orthogonal to andwould facilitate these existing frameworks.
III. S CENE G RAPH M ODELIn the proposed GCN self-localization framework, twotypes of scene graph models are used: the single-view
subimage-level scene graph (SVSL) and the multi-view
image-level scene graph (MVIL), which are described in
Sections III-A and III-B, respectively (Fig. 2).
A. Single-view Subimage-level Scene Graph (SVSL)The SVSL takes as input a single-view scene and converts
it into a subimage-level scene graph. In the implementation,
we use a total of four subimage nodes that correspondto the entire image region [0, 0]×[1080, 800] and threebounding boxes: CENTER [270, 200]×[810, 600], RIGHT[780, 0]×[1080, 800], and LEFT [0, 0]×[300, 800]. As
shown in Fig. 3, in an SVSL graph, the edges extend in a star
shape from the entire image node to the other three subimage
nodes. While this scene graph model requires only a singleview image as an input, the invariance of the graph depends
signiﬁcantly on the invariance of the image segmentation.
This limitation does not affect the MVIL model (III-B).

Fig. 5.

Fig. 4.

Multi-view image-level scene graph (MVIL).

It can be effective to use a semantic segmentation (SS)technique to decompose an image into subimages insteadof ﬁxed bounding boxes. For example, in [2], the methodof decomposing a scene into subimages via SS and connecting the segmented subimages via object-level edges
experimentally worked well under an ideal condition ofground-truth segmentations. However, the good performance
was not replicated in our current implementation of GCN
self-localization. In a preliminary experiment, we attempted
to use a state-of-the-art SS technique [38] instead of the ﬁxed
segmentation strategy, which was signiﬁcantly affected bysegmentation noise.
B. Multi-view Image-level Scene Graph (MVIL)
The MVIL takes as input a view-sequence scene and represents it as an image-level scene graph with multi-attribute
frame image nodes and two types of graph edges: time andattribute edges (Fig. 4). As an example, in experiments, weconsider at most K = 4 different image nodes, which are
obtained by converting an original input RGB image with(K − 1) different image ﬁlters: Canny, depth regression, andSS, as shown in Fig. 4. A time edge connects the nodesof successive image frames with the same attribute. An
attribute edge connects different attribute nodes of the sameimage frame. (K − 1) attribute images are connected to the
RGB image node via attribute edges, yielding a star shapefrom the RGB image node to the (K − 1) attribute image
nodes, as shown in Fig. 4. To facilitate the invariance ofthe time edge, the sampling of image frames is controlled
so that the travel distance between successive image frames(connected by a time edge) becomes constant with regard
to odometry measurements. While a multi-view scene graphrequires as input a view-sequence, it is largely unaffectedby segmentation noise. This is an appealing property of the
MVIL model. The MVIL model is also related to sequencebased approaches such as [39] and [40]. A key advantageof the MVIL model against these existing approaches isthat it is able to process multi-modal input data, as we will
demonstrate in the experimental section.
The implementation details are as follows: We implemented (K − 1) types of attribute images: Canny, depth,
and SS images, which were converted from an original
RGB image by using the Canny edge detector [41], deep
depth regressor [42], and Deeplab v3+ [38], respectively. The
weight parameters of the deep depth regressor and Deeplab
v3+ were pretrained on the KITTI dataset [43] and theKnowledge transfer on node feature descriptor.

Cityscapes dataset [44], respectively. The pixel values of an
SS image were deﬁned by the color map in [44]. The lengthof the view-sequence for the MVIL model was 10 frames,with 2-m intervals.
IV. GCN S ELF - LOCALIZATIONIn this section, we describe the proposed GCLN framework for lightweight and accurate self-localization basedon knowledge transfer (Fig. 2). In the proposed framework, a lightweight representation of the scene graph is
obtained using knowledge transfer from an external teacher
self-localization model. Additionally, the accuracy of selflocalization can be higher than that of the teacher selflocalization model.
A. Knowledge Transfer
In knowledge transfer [45], the prediction results of ateacher model are often used as the dark knowledge totransfer. In particular, we propose the use of the (reciprocal-)rank vector as the representation of such dark knowledge.
Many off-the-shelf self-localization systems (e.g., bag-ofwords systems [15], classiﬁcation systems [46], and mapmatching systems [47]) can be modeled as ranking systems.
Therefore, our (reciprocal-) rank-based scheme has a broader
application area than existing knowledge-transfer schemes,
e.g., those where intermediate signals of the teacher systems
are used as the dark knowledge to transfer.
As an example, in our experimental system, a typicalnearest neighbor (NN) image classiﬁer with a NetVLAD
image descriptor [3] was employed as the teacher model (Fig.
5). The teacher model used a visual image as an input, computed the L2 nearest-neighbor distance from the query image
descriptor to the class-speciﬁc database image descriptors,
and then converted the distance values into a class-speciﬁcrank value vector; a smaller rank value corresponded to abetter degree of matching. Such pairings of the input image
and output rank value vector are used as the dark knowledge
to transfer in our scheme. We observed that a reciprocal-rankvalue vector is a good representation of an attribute-imagenode descriptor, as discussed in Section V.
B. GCN Classiﬁer
This subsection describes the procedure for graph convolution, focusing on the equation for forward propagation. A
scene graph is represented as G = (V, E), where V represents
the set of nodes and E represents the set of edges. Letvi ∈ V denote a node and ei j = (vi , v j ) ∈ E denote an edge
pointing from v j to vi . The graph is deﬁned as an undirected
graph; i.e., whenever ei j exists, e ji exists. The neighborhoodof a node v is deﬁned as N(v) = {u ∈ V |(u, v) ∈ E}. Each

node v has a feature vector h ∈ RD , where D is the number of dimensions of the feature vector. We performed anexperimental ablation study (Section V), in which not only
the class-speciﬁc reciprocal-rank vector but also the otherintermediate representations, such as the original NetVLAD
vector, class-speciﬁc NN-distance vector, and class-speciﬁcrank vector, were considered as the node feature descriptor.
The graph convolution operation takes node vi in thegraph and processes it in the following manner. First, it
receives messages from nodes connected by the edge. Then,the collected messages are summed via the SUM function.
The result is passed through a single-layer fully connectedneural network followed by a nonlinear transformation forconversion into a new feature vector. In this study, we used
the rectiﬁed linear unit (ReLU) operation as the nonlinear
transformation, which is expressed as follows:))( (= ReLU W
hnew
i

∑

hu

.

(1)

u∈N(vi )∪vi

Here, W represents an RD×F weight matrix, and D and F
represent the numbers of dimensions of the node feature
vector before and after the linear transformation, respectively.
The foregoing process can be generalized to the processingof node features in the l-th GCN layer:
))
(
(
(l)

hi = ReLU W(l−1)

∑

(l−1)

hu

.

(2)

u∈N(vi )∪vi

The process was applied to all the nodes in the graph in each
iteration, yielding a new graph that had the same shape as
the original graph but updated node features. The iterative
process was repeated L times, where L represents the IDof the last GCN layer. After the graph node information
obtained in this manner were averaged, the probability value
vector of the prediction for the graph was obtained by applying the fully connected layer and the softmax function. Thisaveraging operation is called “Readout.” For the probability
value vector of the output p, the operation is expressed asfollows:( ())
1
L
p = Softmax FC(3)∑ hu .
|V | u∈V
where hu is a feature of node u after it passes through thelast GCN layer. For implementation, we used the Deep Graph
Library [48] on the Pytorch backend.
V. E XPERIMENTS
We conducted self-localization experiments to conﬁrm theeffectiveness of the proposed method by using the publicly
available Oxford Robotcar Dataset [49].
A. Settings
The Oxford Robotcar Dataset was obtained by a robotic
vehicle-mounted camera when a robot car traveled along thesame route in different seasons and with different weather
and lighting conditions. Table I presents details regarding
the dataset used in this study. The onboard camera used

TABLE IS TATISTICS OF THE DATASET.
date
2015-08-28-09-50-22
2015-10-30-13-52-14
2015-11-10-10-32-52
2015-11-12-13-27-51
2015-11-13-10-28-08

Fig. 6.

weathersunovercast
overcast
cloudsovercast, sun#images
31,85548,19629,35041,47242,968

detour×××◦×

roadworks
×
×
◦
◦
×

Example of place partitioning.

was a PointGreyBumblebeeXB3 (BBX3-13S2C-38) trinocular stereo camera (the center camera, 1280×960×3, 16
Hz). To avoid self-reﬂections and self-occlusions due to thevehicle, we used an image region of 1080×800 pixels (with100 pixels from the left and right and 160 pixels from thebottom removed).
To deﬁne the place class, the workspace of the Oxford
Robotcar Dataset was partitioned into a two-dimensional regular grid of place classes according to the ground-truth global
positioning system coordinates (Fig. 6). More formally, an
area surrounded by 0.001 degree of latitude and longitude
was deﬁned as a one-place class. The number of classes forthese test seasons ranged from 82 to 86. The classes thatexisted only for training in each season pair and the classes
with less than ﬁve images in the area were not used in theexperiments. “Unseen” classes, which existed only in thetest season, were used as-is. The parameters of the NetVLAD
descriptor were trained on the Pittsburgh (Pitts250k) dataset[3].
A subsequence of length 20 [m] obtained by shifting
the ﬁrst image frame by frame was sampled from theentire image sequence and used as training/test samples.
For each dataset, all possible overlapping subsequenceswith travel distance 20 [m] were sampled from the entire
image sequence and used as training/test samples. Those
subsequences that straddle different place classes were removed. For single-view methods, the ﬁrst image frame ofeach subsequence is used as a query input. For multi-view
methods, each subsequence is represented by a length 10
view-sequence with 2-m intervals and used as a query input.
The number of GCN layers L was set as 2. The numberof dimensions of the intermediate representation was 256.
Thus, when the number of classes was C, the number ofdimensions of the feature vectors (from the bottom layer tothe top layer) was C→256→256→C. The node aggregation
method used the SUM operation and the ReLU activation
function. The number of epochs was set as 5. The batch size
was 32, and the learning rate was 0.001. The cross-entropyTABLE II
AVERAGE TOP -1 ACCURACY.
MethodOurs
NetVLADSeqSLAM

Average Top-1 Accuracy
92.4
87.9
2.9

loss function and the Adam optimizer were used.
B. Comparison Methods
We used NetVLAD [3] and SeqSLAM [50] as comparison
methods (Table II). The implementation of NetVLAD wasbased on [51]. NetVLAD was used in a single-view imagelevel self-localization scheme, in which the nearest-neighbormatching of place classes in terms of the Euclidean distance
was performed. SeqSLAM was used as a multi-view imagelevel self-localization scheme. The implementation of SeqSLAM was based on the C++ version of OpenSeqSLAM. The
parameters of SeqSLAM were optimized for the Nordland
dataset, and no parameter manipulation was performed. The
image IDs output by SeqSLAM were converted into the placeclass IDs to which the images belonged, and then the class
IDs were simply used as outputs of the system.
C. Results
Fig. 7 presents example results of the proposed method,where L2 norm nearest neighbor matching is used withthe output of the middle layer of GCN. As shown, theproposed method was robust against illumination changes
and dynamic objects, owing to the Canny and SS image
ﬁlters. However, the proposed method was not suitable forhomogeneous scenery with no distinctive landmarks. This isbecause none of the image ﬁlters employed by the method(i.e., Canny, depth, SS) were robust against homogeneous
scenes. To compensate, prior domain knowledge, e.g., roadmarkings or the road topology, can be used as additionalgraph node descriptors. We plan to investigate this in a future
study.
Computation time for GCN classiﬁcation was 23.8 msec
per graph (Intel (R) Xeon (R) GOLC 6130 CPU @ 2.10
GHz). For the GCN training, the speed was satisfactory (170
sec for a size 31,835 training set) even with CPU. This
indicates that our approach can be implemented even on lowcost hardware with moderate performance, such as that usedby small, inexpensive robots [52].
The results for the SVSL scene graph are presented in Fig.
8. For an ablation study, in addition to the proposed SVSL
scene graph, a naive scene graph without edge connections
was tested. As shown, the performance was better when edge
connections were used.
The results for the proposed and comparison methods
are presented in Figs. 9, 10 and 11. Comparing Figs. 8
and 9 reveals that the MVIL method using the reciprocalrank vector had the best performance. In Figs. 9, 10 and
11, the proposed method employs an MVIL scene graphwith raw RGB, Canny, and SS attribute image nodes (i.e.,
K = 3). First, the result for K = 2 is shown. In this study, we

TABLE IIIP ERFORMANCE RESULTS VERSUS THE GRAPH STRUCTURE .
MethodAttribute edges and Time edges
w/o all edges
w/o attribute edges
w/o time edges
w/o attribute node/edge

Average Top-1 accuracy
92.3
89.0
91.5
88.7
91.7

TABLE IVP ERFORMANCE RESULTS FOR DIFFERENT COMBINATIONS OF K AND
IMAGE FILTERS .
number of nodes
k=2

k=3
k=4

combination
canny
depth
semantic
canny-depth
canny-semantic
depth-semantic
canny-depth-semantic

Average Top-1 accuracy
92.1
91.8
92.3
92.0
92.4
92.1
92.3

investigated which node feature is appropriate, which image
conversion method is compatible with it, and which graphstructure is optimal. Fig. 10 presents the dependencies of the
choice of the attribute feature descriptor on the performance.
Next, Fig. 11 presents the dependencies of the choice of
the attribute image on the performance, where the feature is
ﬁxed to the reciprocal-rank vector, for the case of K = 2.
As shown, the method using a semantic image had thehighest accuracy. Clearly, the proposed method outperforms
the comparison methods, i.e., NetVLAD and SeqSLAM.
Table III presents the results for different graph structures
obtained using the reciprocal-rank method and K = 2 scenegraph structure with the SS attribute image. For nodes
without edge connection, there is no inter-node informationtransmission in the convolution process and thus, the featuretranslation is done independently for each node. As shown,
the As shown, the prediction performance was improved withboth the attribute and time edges, relative to the other graphstructures.
Table IV presents the performance results for different
combinations of image ﬁlters and the following numbers
of ﬁlters: K =2, 3, 4. As shown, the performance was
maximized when K = 3 ﬁlter set was used that consistedof the RGB image, Canny, and SS conditions.
D. Discussion
We now examine why the performance was improved by
the proposed GCLN framework. For the SVSL scene graph,
it is considered that the performance was largely affectedby the degree of invariance of the image segmentation. The
MVIL scene graph was successful for many difﬁcult scenes
where the NetVLAD method often failed. One reason forthis is that knowledge from multiple image frames helped tounderstand the scene structure, which was captured by the
GCN. Additionally, the attribute node inherited the desirable
properties of the multiple attribute images, e.g., robustness against illumination changes (Canny), spatial invarianceFig. 7. Example results. From left to right, the panels show the query scene, the top-ranked DB scene, and the ground-truth DB scene. Green and red
bounding boxes indicate “success” and “failure” examples, respectively.

Fig. 8. Performance results for single-view scene graph with and withoutedge connections.

Fig. 10. Performance results versus the choice of attribute image descriptors(K=2).

Fig. 9.

Performance results for different training and test season pairs.

Fig. 11. Performance results for individual training/test season pairs (K=2).

in non-dynamic scenes (depth), and appearance invarianceagainst seasonal shifts. The proposed method can combine
the strengths of different attribute images in a computationally efﬁcient manner. Moreover, the average performance is
not sensitive to the graph structure, the number of attributeedges, or the combination of attribute images used, indicating
the ﬂexibility of the proposed GCLN framework.

GCN. To this end, a novel teacher-to-student knowledgetransfer scheme based on rank matching was introduced. Experimental results indicated that the proposed framework outperformed the state-of-the-art methods and the teacher selflocalization system. The reciprocal-rank vector was found tobe effective dark knowledge to transfer, and in a future study,
we plan to develop additional knowledge-transfer strategies
for improving the GCN self-localization performance.

VI. C ONCLUSIONSWe presented a framework for enhancing a visual robot
self-localization system using GCN. The proposed GCLN
framework combines the accuracy of state-of-the-art selflocalization systems and the ﬂexibility and efﬁciency of the

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