11institutetext: NVIDIA, Santa Clara, CA
11email<EMAIL_ADDRESS><EMAIL_ADDRESS>
# Redundancy Reduction in Semantic Segmentation of 3D Brain Tumor MRIs

Md Mahfuzur Rahman Siddiquee  Andriy Myronenko

###### Abstract

Another year of the multimodal brain tumor segmentation challenge (BraTS) 2021
provides an even larger dataset to facilitate collaboration and research of
brain tumor segmentation methods, which are necessary for disease analysis and
treatment planning. A large dataset size of BraTS 2021 and the advent of
modern GPUs provide a better opportunity for deep-learning based approaches to
learn tumor representation from the data. In this work, we maintained an
encoder-decoder based segmentation network, but focused on a modification of
network training process that minimizes redundancy under perturbations. Given
a set trained networks, we further introduce a confidence based ensembling
techniques to further improve the performance. We evaluated the method on
BraTS 2021 validation board, and achieved 0.8600, 0.8868 and 0.9265 average
dice for enhanced tumor core, tumor core and whole tumor, respectively. Our
team (NVAUTO) submission was the top performing in terms of ET and TC scores
and within top 10 performing teams in terms of WT scores.

###### Keywords:

Brats Redundancy Reduction Brain Tumor 3D MRI.

##  1 Introduction

This year, 2021 multimodal brain tumor segmentation challenge (BraTS) [2],
boasts a large dataset of 2000 cases. Long gone the days of a modest couple of
hundred image datasets [6, 13]. With a large data size comes more confidence
in the achieved solution to be better generalizible in clinical practice. The
dataset includes data from the previous year challenges, which also implies
that some cases might be very dated (of low image quality), but this can be
considered a positive feature to ensure the robustness of the solution. A
large data size, in theory, should lead to a more accurate solution, but also
requires a large computational resource. Thankfully, modern GPUs, such as as
Nvidia A100 (RTX generation), have substantially improved over the last years
in terms of speed, performance and GPU memory sizes. It is also interesting to
note of the paradigm change, that it is no longer necessary to motivate the
necessity of deep learning based approach here, as every solution in this
challenge is probably deep learning based.

Gliomas are primary brain tumors, which originate from brain cells, whereas
secondary tumors metastasize into the brain from other organs. Gliomas can be
of low-grade (LGG) and high-grade (HGG) subtypes. High grade gliomas are an
aggressive type of malignant brain tumor that grow rapidly, usually require
surgery and radiotherapy and have poor survival prognosis. Magnetic Resonance
Imaging (MRI) is a key diagnostic tool for brain tumor analysis, monitoring
and surgery planning. Usually, several complimentary 3D MRI modalities are
acquired - such as T1, T1 with contrast agent (T1c), T2 and Fluid Attenuation
Inversion Recover (FLAIR) - to emphasize different tissue properties and areas
of tumor spread. For example the contrast agent, usually gadolinium,
emphasizes hyperactive tumor subregions in T1c MRI modality.

Multimodal Brain Tumor Segmentation Challenge (BraTS) aims to evaluate state-
of-the-art methods for the segmentation of brain tumors by providing a 3D MRI
dataset with ground truth tumor segmentation labels annotated by physicians
[6, 11, 5, 3, 4]. This year, BraTS 2021 training dataset included 1251 cases,
each with four 3D MRI modalities (T1, T1c, T2 and FLAIR) rigidly aligned,
resampled to 1x1x1 mm isotropic resolution and skull-stripped. The input image
size is 240x240x155. The data were collected from multiple institutions, using
various MRI scanners. Annotations include 3 tumor subregions: the enhancing
tumor, the peritumoral edema, and the necrotic and non-enhancing tumor core.
The annotations were combined into 3 nested subregions: whole tumor (WT),
tumor core (TC) and enhancing tumor (ET), as shown in Figure 1. Two additional
datasets without the ground truth labels were provided for validation and
testing. The validation dataset (219 cases) allowed multiple submissions and
was designed for intermediate evaluations. The testing dataset (530 cases)
will be analysed blindly using the docker submission, and is used to calculate
the final challenge ranking.

In this work, we describe our approach for 3D brain tumor segmentation from
multimodal 3D MRIs and participate in BraTS 2021 challenge.

##  2 Related work

Previous years of BraTS challenge winners include our work in 2018 [13], using
encoder-decoder based network with asymmetrically large encoder. In 2019,
Jiang et al. [10] used a similar encoder-decoder architecture, but added a
second network to refine the segmentation in a cascade fashion. In 2020,
Isensee et al. [9] proposed modifications to their nnUnet work. The authors
continue to demonstrate that a standard encoder-decoder based architecture can
achieve state of the art results, given the best practices of all components
of the segmentation workflow (pre-processing, normalization, augmentations,
ensembling). Here, we generally follow our encoder-decoder based network from
[13] as a backbone, but modify the training and ensembling strategies.

##  3 Methods

We used SegResNet from MONAI [1, 13] with encoder-decoder based CNN
architecture. We switched to Instance Normalization [14], as it has a lightly
lower memory footprint compared to Group Normalization (GN) [15], for
equivalent performance. Briefly speaking, the encoder part uses ResNet [8]
blocks, where each block consists of two convolutions with normalization and
ReLU, followed by additive identity skip connection. We progressively downsize
image dimensions by 2 and simultaneously increase feature size by 2. Each
decoder level begins with upsizing followed by an addition of encoder output
of the equivalent spatial level. The end of the decoder has the same spatial
size as the original image, and the number of features equal to the initial
input feature size, followed by 1x1x1 convolution into 3 channels and a
sigmoid function. See Table 1 for the details.

Table 1: Backbone network structure, where IN stands for group normalization, Conv - 3x3x3 convolution, AddId - addition of identity/skip connection. Name | Ops | Repeat
---|---|---
InitConv | Conv | 1
EncoderBlock0 | IN,ReLU,Conv,IN,ReLU,Conv, AddId | 1
EncoderDown1 | Conv stride 2 | 1
EncoderBlock1 | IN,ReLU,Conv,IN,ReLU,Conv, AddId | 2
EncoderDown2 | Conv stride 2 | 1
EncoderBlock2 | IN,ReLU,Conv,IN,ReLU,Conv, AddId | 2
EncoderDown3 | Conv stride 2 | 1
EncoderBlock3 | IN,ReLU,Conv,IN,ReLU,Conv, AddId | 4
DecoderUp2 | UpConv, +EncoderBlock2 | 1
DecoderBlock2 | IN,ReLU,Conv,IN,ReLU,Conv, AddId | 1
DecoderUp1 | UpConv, +EncoderBlock1 | 1
DecoderBlock1 | IN,ReLU,Conv,IN,ReLU,Conv, AddId | 1
DecoderUp0 | UpConv, +EncoderBlock0 | 1
DecoderBlock0 | IN,ReLU,Conv,IN,ReLU,Conv, AddId | 1
DecoderEnd | IN,ReLU, Conv1, Sigmoid | 1

###  3.1 Redundancy Reduction

We would like to encourage structure on the learned feature representations of
our network. Firstly, we want to enforce invariance of the result under
perturbations. Generally, it is common to use image augmentations, such as
intensity modifications or spatial transforms, to implicitly enforce network
robustness to such image perturbations. However, this alone does not often
lead to a similar feature representation under perturbations, even if the
final segmentation masks are similar. In semi-supervised learning, people
adopted such method as contrasting coding of SimCLR [7] to enforce consistency
of learned features under perturbations. Contrastive coding requires large
number of negative samples/batches, which is too computationally expensive for
3D images. Secondly, we also want another useful property of the learned image
features: minimal redundancy. Loosely speaking, we want different samples to
have different learned representation with minimal information overlap. For
these reason, we adopted the loss term from Barlow Twins [16], which is:

$\mathbf{L}_{BT}=\mathbf{L}_{invariance}+\mathbf{L}_{redundancy}$ (1)

Unlike the original paper concerning classification, our adaptation is for the
segmentation which requires some modifications. For example, when training
with a 3D batch size of 1, we copy it and augment it each copy independently,
forming a batch of 2. For augmentations we use, both intensity and spatial
augmentations. We then attach a projection branch to the output feature
dimension (one level before the final normalization). The projection branch
first average pools the features by a factor of 16, for two reasons: the
output features are of the original image size, and it’s too computationally
expensive to use them directly, secondly spatial augmentation transforms would
produce geometrical image misalignment between the two images, and average
pooling ensures that the pooled features are roughly of the same spatial
content. After pooling the newly formed features are reshaped to form a large
batch of 1D features.

At the stage we proceed with the projection branch (3 layer MLP) and compute
the empirical cross-correlation matrix $C$ between all combinations of spatial
regions [16]:

$C_{ij}=\frac{\sum_{b}z^{A}_{b,i}z^{B}_{b,j}}{\sqrt{\sum_{b}(z^{A}_{b,i})^{2}}\sqrt{\sum_{b}(z^{B}_{b,j})^{2}}}$
(2)

where b indexes batch samples and i,j index the vector dimension of the
networks’ outputs. C is a square matrix with size the dimensionality of the
network’s output, and with values comprised between -1 (i.e. perfect anti-
correlation) and 1 (i.e. perfect correlation).

Unlike the original work, which uses a batch of many different 2D images, our
cross-correlation matrix is based on the various regions of the same image
under permutations. Based on the cross-correlation matrix, we can compute a
differentiable loss:

$\mathbf{L}_{BT}=\sum(1-C_{ii})^{2}+\lambda\sum_{i\neq j}C_{ij}^{2}$ (3)

where the first part enforces invariance of learned feature representations
from the same spatial regions under perturbations, and second term reduces
redundancy between different spatial regions. We used $\lambda=0.005$ weight,
to balance the parts, as proposed in the original paper. The projection branch
is discarded during inference. We use this loss in additional to the main soft
Dice loss [12]:

$\mathbf{L}_{dice}=1-\frac{2*\sum p_{true}*p_{pred}}{\sum p_{true}^{2}+\sum
p_{pred}^{2}+\epsilon}$ (4)

where $p_{true}$ is a ground truth binary mask, and $p_{pred}$ is the
predicted probability (after sigmoid) per class.

###  3.2 Confidence based ensembling

Given a trained set of models, ensembling is a popular technique to boost the
performance, typically by averaging the probabilities of predictions.
Alternatively one can employ a geometrical mean (instead of standard mean) to
combine the probabilities. We take it one step further and design a technique
to adaptively average the probability maps.

Assuming we know the confidence of the solution/prediction result of each
model for a given image, then we could use the subset of the probability maps
with the top confidence for ensembling (or we can use the weight mean of all
such maps). We found that using the top N/2 probabilities (with equal weights)
generally gives the best performance, where N is the number of all maps before
the ensembling.

Estimation of the confidence measure of the given segmentation probability map
is non-trivial. We propose a heuristic for such estimate as the average
probability value of the segmented region. Such heuristic is based on the
observation that given two probability maps of the same final segmentation
volume, the one with the highest average probability is usually more accurate.
This assumption is not true when different models produce substantially
different region sizes, or if the trained model were very different to compare
directly. In our experiment, we found such heuristic consistently improves the
ensembling performance.

###  3.3 Optimization

We use AdamW optimizer with initial learning rate of $\alpha_{0}=10^{-4}$ and
progressively decrease it according to Cosine schedule. We use $10^{-5}$
weight decay and no dropout.

###  3.4 Data prepossessing and augmentation

We normalize all input images to have zero mean and unit std (based on non-
zero voxels only). We also apply a random axis mirror flip (for all 3 axes)
with a probability $0.5$. After this we copy the image, and apply the
intensity and spatial transforms.

##  4 Results

Figure 1: A typical segmentation example with true and predicted labels
overlaid over T1c MRI axial, sagittal and coronal slices. The whole tumor (WT)
class includes all visible labels (a union of green, yellow and red labels),
the tumor core (TC) class is a union of red and yellow, and the enhancing
tumor core (ET) class is shown in yellow (a hyperactive tumor part).

We implemented our network in MONAI 111https://github.com/Project-MONAI/MONAI
and trained it on 4 Nvidia V100 32GB GPUs using 5-fold cross-validation.
During training we used a random crop of size 192x192x144, which ensures that
most image content remains within the crop area. We concatenated 4 available
3D MRI modalities into the 4 channel image as an input. We train it on 4 GPU
for 300 epochs in about 24hr. The output of the network is 3 nested tumor
subregions (after the sigmoid).

Typically, the output result, even of a single model, is accurate as shown in
Figure 1, however several cases still remain segmented imprecisely. Figure 2
shows an example of an incorrectly over-segmented whole tumor (WT) region,
which is spilled over on the right side of the brain, most likely because the
underlying MRI (Flair) has substantially higher intensity values in that
region. More variability in training examples might have helped to solve the
issue, or integration of anatomical knowledge of e.g. ”symmetrical highlights
around ventricles are unlikely to be a tumor” , but such information is rather
complicated to put inside of the network.

Figure 2: An example of the incorrectly over-segmented result. The whole tumor
(WT) in green is incorrectly spilled over on the right side of the brain, most
likely because the underlying MRI (Flair modality) has high intensity regions
which usually corresponds to the tumor.

We report the cross-validation results using our own 5-fold splits of the
training portion of the data in Table 2 and the evaluated results of the BraTS
2021 validation set (219 cases) in Table 3. To get the validation results, we
uploaded our segmentation masks to the BraTS 2021 server for evaluation, since
the ground truth is not provided. Compared to the validation results, our own
cross-validation per fold results are very similar, but 1-2% higher. A slight
disagreement is normal, and due to a variability of data in the validation
sets, and due to the fact that we are able to select the best checkpoint using
our own 5-folds.

Table 2: 5-fold cross-validation results using our own random data splits on BraTS 2021 training dataset. Mean Dice: EN - enhancing tumor core, WT - whole tumor, TC - tumor core. Fold | ET | TC | WT
---|---|---|---
0 | $0.8759\pm 0.007$ | $0.9152\pm 0.009$ | $0.9332\pm 0.011$
1 | $0.8993\pm 0.012$ | $0.9213\pm 0.007$ | $0.9379\pm 0.005$
2 | $0.8880\pm 0.006$ | $0.9220\pm 0.013$ | $0.9313\pm 0.014$
3 | $0.8902\pm 0.008$ | $0.9258\pm 0.007$ | $0.9351\pm 0.008$
4 | $0.8847\pm 0.011$ | $0.9198\pm 0.013$ | $0.9374\pm 0.005$
Table 3: BraTS 2021 validation dataset results. Mean Dice and Hausdorff95 measurements of the proposed segmentation method. EN - enhancing tumor core, WT - whole tumor, TC - tumor core. | Dice | Hausdorff95
---|---|---
Validation dataset | ET | TC | WT | ET | TC | WT
Our result (NVAUTO) | 0.8600 | 0.8868 | 0.9265 | 9.0541 | 5.8409 | 3.6009

##  5 Discussion and Conclusion

In this work, we described a semantic segmentation network for brain tumor
segmentation from multimodal 3D MRIs for BraTS 2021 challenge. We have
introduced redundancy reduction to enforce structure on the learned features,
and demonstrated confidence based ensembling technique. Our BraTS 2021 final
validation dataset results were 0.8600, 0.8868 and 0.9265 average dice for
enhanced tumor core, tumor core and whole tumor, respectively. As of Aug 21,
2021, when the validation server of Brats 2021 stopped accepting new
submissions, our results represented the top performing team in terms of the
ET and TC dice scores, and were within the top 10 teams in terms of the WT
dice score.

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##  Appendix A Basic information for observational facilities used

We report the basic information for observational facilities in Table 6, which
were used for the five ILRTs.

Table 6: Information on the instrumental setups.

Code | Diameter | Telescope | Instrument | Site
---|---|---|---|---
| $\mathrm{m}$ |  |  |
QHY9 | 0.35 | Celestron C14 35-cm reflector | QHY-9 | Xingming Observatory, Xinjiang, China
EM01∗ | 0.40 | LCO (FTN site) | EM01 | LCO node at Haleakala Observatory, Hawaii, USA
PROMPT3/5 | 0.41 | PROMPT Telescope | Apogee Alta | Cerro Tololo Inter-American Observatory, Cerro Tololo, Chile
TRAPPIST | 0.60 | TRAPPIST-S Telescope | FLI ProLine | ESO La Silla Observatory, La Silla, Chile
Moravian | 0.67/0.92 | Schmidt Telescope | Moravian | Osservatorio Astronomico di Asiago, Asiago, Italy
SBIG | 0.67/0.92 | Schmidt Telescope | SBIG | Osservatorio Astronomico di Asiago, Asiago, Italy
fl03∗ | 1.00 | LCO (LSC site) | Sinistro | LCO node at Cerro Tololo Inter-American Observatory, Cerro Tololo, Chile
fl05∗ | 1.00 | LCO (ELP site) | Sinistro | LCO node at McDonald Observatory, Texas, USA
fl06∗ | 1.00 | LCO (CPT site) | Sinistro | LCO node at South African Astronomical Observatory, Cape Town, South Africa
fl12∗ | 1.00 | LCO (COJ site) | Sinistro | LCO node at Siding Spring Observatory, New South Wales, Australia
B$\&$C | 1.22 | Galileo Telescope | B$\&$C | Osservatorio Astronomico di Asiago, Asiago, Italy
ANDICAM-CCD | 1.30 | SMARTS Telescope | ANDICAM | Cerro Tololo Inter-American Observatory, Cerro Tololo, Chile
ANDICAM-IR | 1.30 | SMARTS Telescope | ANDICAM | Cerro Tololo Inter-American Observatory, Cerro Tololo, Chile
AFOSC | 1.82 | Copernico Telescope | AFOSC | Osservatorio Astronomico di Asiago, Asiago, Italy
IO:O | 2.00 | Liverpool Telescope | IO:O | Observatorio Roque de Los Muchachos, La Palma, Spain
RATCam | 2.00 | Liverpool Telescope | RATCam | Observatorio Roque de Los Muchachos, La Palma, Spain
SupIRCam | 2.00 | Liverpool Telescope | SupIRCam | Observatorio Roque de Los Muchachos, La Palma, Spain
WFCCD | 2.50 | Ir$\rm{\acute{e}}$n$\rm{\acute{e}}$e du Pont Telescope | WFCCD | Las Campanas Observatory, Atacama Region, Chile
ALFOSC | 2.56 | Nordic Optical Telescope | ALFOSC | Observatorio Roque de Los Muchachos, La Palma, Spain
NOTCam | 2.56 | Nordic Optical Telescope | NOTCam | Observatorio Roque de Los Muchachos, La Palma, Spain
EFOSC2 | 3.58 | New Technology Telescope | EFOSC2 | ESO La Silla Observatory, La Silla, Chile
SOFI | 3.58 | New Technology Telescope | SOFI | ESO La Silla Observatory, La Silla, Chile
LRS | 3.58 | Telescopio Nazionale Galileo | LRS | Observatorio Roque de Los Muchachos, La Palma, Spain
NICS | 3.58 | Telescopio Nazionale Galileo | NICS | Observatorio Roque de Los Muchachos, La Palma, Spain
ISIS | 4.20 | William Hershel Telescope | ISIS | Observatorio Roque de Los Muchachos, La Palma, Spain
LDSS | 6.50 | Magellan II - Clay Telescope | LDSS | Las Campanas Observatory, Atacama Region, Chile
GMOS | 8.10 | Gemini South Telescope | GMOS-S | Gemini Observatory, Cerro Pachon, Chile
OSIRIS | 10.40 | Gran Telescopio CANARIAS | OSIRIS | Observatorio Roque de Los Muchachos, La Palma, Spain

$*$ They are distributed globally at different sites and form part of the LCO
global telescope network (Brown et al. 2013).

##  Appendix B Reddenings and distances adopted for SNe II

In this section, the reddenings and distances adopted for the comparison SNe
II are reported in Table 7, along with their respective references.

Table 7: Reddenings and distances of SN 2018zd, SN 2018hwm, SN 2015bf, SN
1999br, and SN 2005cs.

Object | Distance | Distance Modulus | $E(B-V)_{\mathrm{Gal}}$ | $E(B-V)_{\mathrm{Host}}$ | Sources
---|---|---|---|---|---
| ($\mathrm{Mpc}$) | ($\mathrm{mag}$) | ($\mathrm{mag}$) | ($\mathrm{mag}$) | Codes
SN 2018zd | 18.4 (4.5) | 31.32 (0.48) | 0.085 | 0.085 | 1
SN 2018hwm | 52 (5) | 33.58 (0.19) | 0.003 | 0 | 2
SN 2015bf | 60.1 (1.4) | 33.89 (0.05) | 0.059 | 0.089 | 3
SN 1999bra | 15.63 | 30.97 | 0.021 | 0 | 4
SN 2005cs | 8.4 (0.5) | 29.62 (0.15) | 0.031 | 0.032 | 5

$Notes$: References for each object are labelled by numbers in the last
column. The uncertainties are reported in the parentheses.
1 = Zhang et al. (2020); 2 = Reguitti et al. (2021); 3 = Lin et al. (2021); 4
= Pastorello et al. (2004); 5 = Pastorello et al. (2006).
a The distance has been rescaled to $H_{0}=73$
$\rm{km}\,s^{-1}$$\rm{Mpc}^{-1}$. The reddening has been updated to the value
in Schlafly & Finkbeiner (2011).

##  Appendix C Photometric data of ILRTs

The photometric data of five ILRTs and associated errors are reported in this
section. In addition, black body parameters and SED evolution of individual
ILRT AT 2010dn are presented in Table 11 and Figure 17, respectively. Our
observations will be made public via the Weizmann Interactive Supernova Data
Repository (WISeREP; Yaron & Gal-Yam 2012).

Table 8: Optical ($BVuriz$) photometric measurements of AT 2010dn.

Date | MJD | Phasea |  $B$(err) |  $V$(err) |  $u$(err) |  $r$(err)bc |  $i$(err)b |  $z$(err) | Instrument
---|---|---|---|---|---|---|---|---|---
20010302 | 51970.50 | -3384.4 | – |  $>$24.1 | – | – | – | – | 1
20090330 | 54921.11 | -433.8 | – | – | – |  $>$19.0 | – | – | 2
20100521 | 55338.00 | -16.9 | – | – | – |  $>$18.0 | – | – | 2
20100531 | 55348.04 | -6.9 | – | – | – | 17.546(0.123) | – | – | 2
20100601 | 55348.98 | -5.9 | – | – | – | 17.407(0.211) | – | – | 2
20100601 | 55349.45 | -5.4 | – | – | – | 17.593(0.172) | – | – | ALFOSC
20100602 | 55350.36 | -4.5 | – | – | – | 17.41 | – | – | 3
20100603 | 55350.65 | -4.2 | – | 17.4 | – | – | – | – | 4
20100603 | 55350.99 | -3.9 | – | – | – | 17.412(0.266) | – | – | 2
20100603 | 55351.40 | -3.5 | 18.036(0.028) | 17.649(0.051) | 18.780(0.105) | 17.465(0.040) | 17.379(0.043) | – | LRS
20100605 | 55352.85 | -2.0 | 17.923(0.036) | 17.411(0.044) | 18.700(0.206) | 17.346(0.040) | 17.260(0.036) | 17.252(0.065) | EM01
20100607 | 55355.42 | +0.5 | 17.781(0.046) | 17.298(0.047) | 18.677(0.080) | 17.215(0.060) | 17.292(0.040) | – | LRS
20100609 | 55357.40 | +2.5 | – | – | – | 17.264(0.167) | – | – | ALFOSC
20100611 | 55359.40 | +4.5 | 18.102(0.034) | 17.584(0.017) | – | 17.477(0.037) | 17.370(0.017) | – | RATCam
20100611 | 55359.43 | +4.5 | 18.066(0.047) | 17.481(0.092) | – | 17.424(0.086) | 17.347(0.052) | – | LRS
20100612 | 55360.41 | +5.5 | 18.074(0.016) | 17.607(0.029) | – | 17.498(0.018) | 17.386(0.038) | – | RATCam
20100613 | 55361.45 | +6.6 | 18.177(0.021) | 17.638(0.025) | 18.990(0.207) | 17.490(0.032) | 17.430(0.039) | 17.486(0.073) | RATCam
20100616 | 55363.84 | +8.9 | 18.141(0.053) | 17.663(0.031) | 19.158(0.358) | 17.552(0.034) | 17.467(0.038) | 17.366(0.048) | EM01
20100616 | 55364.39 | +9.5 | – | – | – | 17.669(0.248) | – | – | LRS
20100617 | 55365.40 | +10.5 | 18.139(0.028) | 17.730(0.025) | 19.237(0.114) | 17.605(0.057) | 17.495(0.040) | 17.376(0.060) | RATCam
20100618 | 55366.38 | +11.5 | 18.294(0.029) | 17.790(0.028) | – | 17.607(0.031) | 17.486(0.039) | – | RATCam
20100620 | 55367.82 | +12.9 | 18.261(0.041) | 17.701(0.033) | 19.233(0.148) | 17.700(0.040) | 17.442(0.037) | 17.378(0.068) | EM01
20100621 | 55368.79 | +13.9 | 18.325(0.051) | 17.752(0.025) | 19.186(0.109) | 17.650(0.049) | 17.550(0.046) | 17.432(0.072) | EM01
20100623 | 55370.80 | +15.9 | 18.367(0.096) | 17.797(0.090) | – | 17.665(0.048) | 17.419(0.072) | 17.313(0.088) | EM01
20100623 | 55371.41 | +16.5 | 18.422(0.022) | 17.850(0.033) | 19.322(0.137) | 17.687(0.049) | 17.550(0.039) | 17.428(0.056) | RATCam
20100625 | 55373.41 | +18.5 | 18.449(0.039) | 17.907(0.036) | 19.405(0.160) | 17.619(0.058) | 17.504(0.039) | 17.445(0.058) | RATCam
20100626 | 55373.80 | +18.9 | 18.468(0.089) | 17.810(0.049) | – | 17.667(0.029) | 17.574(0.046) | 17.395(0.074) | EM01
20100627 | 55374.80 | +19.9 | 18.489(0.054) | 17.930(0.044) | – | 17.854(0.047) | 17.637(0.043) | 17.374(0.073) | EM01
20100628 | 55375.79 | +19.9 | – | – | – | – | – | 17.465(0.174) | EM01
20100628 | 55376.39 | +21.5 | 18.699(0.052) | 17.934(0.019) | 19.612(0.123) | 17.828(0.012) | 17.558(0.044) | 17.473(0.062) | RATCam
20100629 | 55377.42 | +22.5 | 18.658(0.030) | 17.922(0.027) | 19.559(0.130) | 17.799(0.010) | 17.553(0.027) | 17.466(0.115) | RATCam
20101117 | 55517.18 | +162.3 | 22.555(0.101) | 22.019(0.040) | – | 21.461(0.066) | 20.618(0.053) | – | LRS
20101213 | 55543.08 | +188.2 | – | 22.057(0.116) | – | 21.485(0.132) | 20.679(0.075) | – | LRS
20101231 | 55561.20 | +206.3 | – | 22.053(0.149) | – | 21.494(0.101) | 20.721(0.125) | – | LRS
20110105 | 55566.14 | +211.3 | – | – | – | 21.542(0.036) | – | – | LRS
20111228 | 55923.11 | +568.2 |  $>$23.0 |  $>$22.9 | – |  $>$22.8 | – | – | AFOSC

a Phases are relative to the $r$-band maximum light: MJD=55354.9.

b Johnson-Cousins $R$ and $I$ filter data were converted to Sloan $r$ and $i$
band magnitudes respectively, following the relations of Jordi et al. (2006)

c Unfiltered data obtained by amateur astronomers, calibrated to Sloan
$r$-band magnitudes.

$1$ This approximation is based on the similar throughputs between wide
filters F555W/F814W and $V$/$I$ . Original data published by Berger (2010),
and reported to Johnson-Cousins $V$ and $I$ ($I>$24.9 $\mathrm{mag}$)
magnitudes.

$2$ Amateur data (K. Itagaki) scaled to $r$ band .

$3$ Bright Supernova website
(http://www.rochesterastronomy.org/sn2010/index.html#2010dn; Observation: J.
Nicolas).

$4$ Bright Supernova website
(http://www.rochesterastronomy.org/sn2010/index.html#2010dn; Observation: J.
Brimacombe).

Table 9: NIR ($JHK$) photometric measurements of AT 2010dn.

Date | MJD | Phasea |  $J$(err) |  $H$(err) |  $K$(err) | Instrument
---|---|---|---|---|---|---
20100606 | 55353.89 | -1.0 | 16.611(0.067) | 15.690(0.065) | – | SupIRCam
20100607 | 55354.89 | +0.0 | 16.412(0.133) | 15.704(0.053) | 15.278(0.068) | NICS
20100607 | 55354.96 | +0.1 | 16.490(0.091) | 15.703(0.119) | – | SupIRCam
20100611 | 55358.89 | +4.0 | 16.491(0.064) | 15.753(0.066) | – | SupIRCam
20100614 | 55361.90 | +7.0 | 16.564(0.095) | 15.830(0.091) | – | SupIRCam
20100627 | 55374.89 | +20.0 | 16.744(0.340) | 15.838(0.082) | – | SupIRCam
20100629 | 55376.90 | +22.0 | 16.758(0.192) | 15.871(0.112) | – | SupIRCam
20101201 | 55531.22 | +176.3 | 18.974(0.167) | 17.774(0.152) | 16.868(0.128) | NICS
20101224 | 55554.14 | +199.2 | 19.341(0.127) | 18.053(0.141) | 17.465(0.101) | NICS

a Phases are relative to the $r$-band maximum light: MJD=55354.9.

Table 10: Spitzer IRAC photometry of AT 2010dn (AB mag). Uncertainties are
given in parentheses.

Date | MJD | Phasea | CH1 (3.6 $\mu$m) | CH2 (4.5 $\mu$m)
---|---|---|---|---
|  | (d) | (mag) | (mag)
20100708 | 55385.5 | $+30.6$ | 16.88 (0.01) | 16.76 (0.01)
20101230 | 55560.6 | $+205.7$ | 18.24 (0.03) | 17.94 (0.02)
20110203 | 55595.7 | $+240.8$ | 18.04 (0.03) | 17.78 (0.01)
20120114 | 55940.8 | $+585.9$ | 18.33 (0.03) | 18.04 (0.02)
20120616 | 55094.9 | $+740.0$ | 18.83 (0.05) | 18.30 (0.02)
20140130 | 56687.4 | $+1332.5$ | 21.39 (0.45) | 20.09 (0.12)
20140303 | 56719.1 | $+1364.2$ | 20.99 (0.33) | 20.00 (0.11)
20140703 | 56841.0 | $+1486.1$ | 22.12 (0.76) | 20.25 (0.13)
20140706 | 56844.5 | $+1489.6$ | 21.76 (0.59) | 20.24 (0.13)
20150211 | 57064.9 | $+1710.0$ | 22.44 (0.93) | 21.12 (0.28)

a Phases are relative to the $R/r$-band maximum (MJD=55354.9).

Table 11: Parameters of blackbody fit to the uBVrizJHK bands of AT 2010dn.
Uncertainties are given in parentheses.

Date | MJD | Phasea | Luminosity (hot) | Temperature (hot) | Radius (hot)
---|---|---|---|---|---
|  | (d) | (1039erg s-1) | (K) | (1013 cm)
20100603 | 55351.40 | $-3.5$ | 66.6 (28.0) | 6350 (320) | 24.0 (5.1)
20100605 | 55352.85 | $-2.0$ | 75.5 (10.1) | 6405 (100) | 25.1 (1.7)
20100607b | 55354.89 | $0.0$ | 75.2 (37.5) | 6490 (1200) | 24.4 (12.2)
20100607 | 55355.42 | $+0.5$ | 78.8 (34.5) | 6460 (360) | 25.2 (5.5)
20100611 | 55358.89 | $+4.0$ | 72.4 (26.9) | 6290 (295) | 25.5 (4.7)
20100611 | 55359.40 | $+4.5$ | 69.7 (32.4) | 6035 (350) | 27.1 (6.3)
20100613 | 55361.45 | $+6.6$ | 63.7 (17.8) | 6075 (200) | 25.6 (3.6)
20100617 | 55365.40 | $+10.5$ | 59.6 (26.2) | 6090 (310) | 24.6 (5.4)
20100623 | 55371.41 | $+16.5$ | 54.3 (9.5) | 5795 (110) | 26.0 (2.3)
20100628 | 55376.39 | $+21.5$ | 48.8 (10.7) | 5390 (135) | 28.5 (3.1)
20101117 | 55517.18 | $+162.3$ | 3.5 (5.1) | 3380 (420) | 19.3 (14.2)
20101201b | 55531.22 | $176.3$ | 3.2 (1.6) | 3420 (170) | 18.2 (9.1)
20101224b | 55554.14 | $199.2$ | 2.8 (1.4) | 3540 (280) | 15.9 (8.0)

a Phases are relative to the $r$-band maximum light curve (MJD=55354.9).
b Data are obtained by fitting a double black body function, but only the
first hot-component parameters are reported. The second warm component has
large uncertainties because its data are incompletely sampled.

Figure 17: SED evolution of AT 2010dn. The lines are the best-fit BBs, which
are overplotted on each SED. Blue lines are the fits of the single BB, while
red lines are the fits of the double BB. The epochs marked to the right of
each SED are relative to the $r$-band maximum. Each SED has been sifted by an
arbitrary constant for clarity.

Table 12: Optical ($UBVRI$) photometric measurements of AT 2012jc.

Date | MJD | Phasea |  $U$(err) |  $B$(err) |  $V$(err) |  $R$(err) |  $I$(err) | Instrument
---|---|---|---|---|---|---|---|---
20120313 | 55999.27 | -24.2 | – | – | – |  $>$19.9 | – | PROMPT3/5b
20120317 | 56003.39 | -20.1 | – | – |  $>$19.5 | – | – | 1
20120327 | 56013.49 | -10.0 | – | – | 18.7 | – | – | 1
20120328 | 56014.07 | -9.4 | – | – | 18.5 | – | – | 1
20120329 | 56015.06 | -8.4 | 20.308(0.114) | 18.823(0.022) | 18.206 (0.027) | 17.855 (0.031) | 17.460 (0.058) | RATCam
20120329 | 56015.14 | -8.4 | – | 18.744(0.053) | 18.259 (0.044) | 17.924 (0.034) | 17.521 (0.129) | AFOSC
20120329 | 56015.35 | -8.2 | – | – | 18.0 (0.1) | – | – | 2
20120331 | 56017.26 | -6.2 | – | 18.390(0.113) | 17.888 (0.051) | 17.503 (0.064) | 17.129 (0.056) | PROMPT3
20120412 | 56029.24 | +5.7 | – | – | 17.776 (0.069) | 17.403 (0.057) | 17.102 (0.045) | PROMPT3/5
20120414 | 56031.37 | +7.9 | – | 18.422(0.020) | 17.901 (0.020) | 17.564 (0.013) | 17.164 (0.029) | EFOSC2
20120415 | 56032.41 | +8.9 | – | – | – | 17.614 (0.062) | – | PROMPT3/5
20120416 | 56033.24 | +9.7 | – | – | 17.904 (0.055) | 17.561 (0.059) | 17.239 (0.049) | PROMPT3/5
20120416 | 56033.97 | +10.5 | 19.391(0.093) | 18.494(0.028) | 17.902 (0.029) | 17.552 (0.032) | 17.285 (0.112) | RATCam
20120417 | 56034.05 | +10.6 | – | 18.443(0.034) | 17.947 (0.030) | 17.591 (0.017) | 17.287 (0.055) | AFOSC
20120417 | 56034.19 | +10.7 | – | – | 17.900 (0.069) | 17.634 (0.056) | 17.201 (0.067) | PROMPT3/5
20120421 | 56038.25 | +14.8 | – | 18.694(0.062) | 18.064 (0.049) | 17.825 (0.084) | 17.445 (0.057) | PROMPT3/5
20120422 | 56039.01 | +15.5 | 19.917(0.109) | 18.598(0.024) | 18.117 (0.025) | 17.856 (0.031) | 17.511 (0.053) | RATCam
20120425 | 56042.11 | +18.6 | – | – | 18.478 (0.109) | 18.094 (0.168) | 17.710 (0.126) | SBIG
20120501 | 56048.17 | +24.7 | – | 19.011(0.084) | 18.436 (0.080) | 18.083 (0.055) | 17.649 (0.071) | PROMPT3/5
20120501 | 56048.20 | +24.7 | – | 19.155(0.013) | 18.479 (0.018) | – | – | ALFOSC
20120501 | 56048.38 | +24.9 | – | 19.064(0.031) | 18.487 (0.032) | 18.112 (0.029) | 17.696 (0.074) | EFOSC2
20120502 | 56049.21 | +25.7 | – | 19.134(0.113) | 18.485 (0.088) | 18.073 (0.058) | 17.647 (0.094) | PROMPT3/5
20120509 | 56056.10 | +32.6 | – | 19.386(0.033) | 18.595 (0.035) | 18.154 (0.076) | 17.700 (0.088) | LRS
20120515 | 56062.11 | +38.6 | 21.101(0.212) | 19.560(0.039) | 18.743 (0.044) | 18.292 (0.050) | 17.701 (0.226) | RATCam
20120515 | 56062.24 | +38.7 | – | – | 18.707 (0.068) | 18.226 (0.072) | 17.647 (0.042) | PROMPT3/5
20120520 | 56067.18 | +43.7 | – | – | – | – | 17.788 (0.052) | PROMPT3/5
20120521 | 56068.17 | +44.7 | – | 19.710(0.132) | 18.807 (0.068) | 18.325 (0.078) | 17.819 (0.035) | PROMPT3/5
20120601 | 56079.97 | +56.5 |  $>$21.3 | 20.142(0.111) | 19.217 (0.051) | 18.699 (0.058) | 18.089 (0.057) | RATCam
20120603 | 56081.11 | +57.6 | – | – | – | 18.804 (0.154) | – | PROMPT3/5b
20120603 | 56081.96 | +58.5 |  $>$21.3 | 20.196(0.148) | 19.263 (0.093) | 18.741 (0.040) | 18.115 (0.079) | RATCam
20120620 | 56098.24 | +74.7 | – | 20.501(0.148) | 19.512 (0.101) |  $>$19.7 | – | TRAPPIST

a Phases are relative to the $R$-band maximum light: MJD=56023.5.

b These unfiltered data were reported to Johnson-Cousins $R$ magnitudes, as
suggested by the quantum efficiency of the CCD.

$1$ Observations from The Astronomer’s Telegram (ATel, No. 4004; see Howerton
et al. 2012).

$2$ Bright Supernova website
(http://www.rochesterastronomy.org/sn2012/index.html#PSNJ14535395+0334049;
Observation: J. Brimacombe)

Table 13: Optical ($UBVRI$) photometric measurements of AT 2013lb.

Date | MJD | Phasea |  $U$(err) |  $B$(err) |  $V$(err) |  $R$(err) |  $I$(err) | Instrument
---|---|---|---|---|---|---|---|---
20120624 | 56102.05 | -222.4 | – | – | – |  $>$19.2 | – | PROMPT35b
20130127 | 56319.34 | -5.2 | – | – | – | 18.897(0.138) | – | PROMPT35b
20130131 | 56323.34 | -1.2 | – | – | – | 18.728(0.099) | – | PROMPT35b
20130204 | 56327.36 | +2.9 | – | – | – | 18.601(0.143) | – | PROMPT35b
20130204 | 56327.41 | +2.9 | – | – | – |  $>$18.3 | – | 1
20130207 | 56330.20 | +5.7 | – | – | 19.132(0.144) | 18.833(0.078) | 18.422(0.090) | AFOSC
20130207 | 56330.39 | +5.9 | – | – | 19.143(0.035) | – | – | EFOSC2
20130208 | 56331.23 | +6.7 | – | – | – | 18.859(0.029) | 18.450(0.038) | RATCam
20130209 | 56332.28 | +7.8 | – | – | 19.237(0.035) | – | – | EFOSC2
20130211 | 56334.23 | +9.7 | – | – | – | 18.998(0.030) | 18.466(0.035) | RATCam
20130215 | 56338.28 | +13.8 | – | 19.878(0.046) | 19.368(0.029) | 18.882(0.043) | 18.455(0.064) | ANDICAM-CCD
20130218 | 56341.23 | +16.7 | 19.541(0.160) | 19.997(0.060) | – | 19.005(0.037) | 18.415(0.038) | RATCam
20130218 | 56341.32 | +16.8 | – | 19.963(0.047) | 19.444(0.034) | 18.888(0.062) | 18.346(0.068) | ANDICAM-CCD
20130220 | 56343.30 | +18.8 | – | 19.937(0.042) | 19.350(0.031) | 19.050(0.031) | 18.474(0.042) | ANDICAM-CCD
20130221 | 56344.22 | +19.7 |  $>$19.9 | 19.998(0.046) | 19.307(0.034) | 18.987(0.050) | 18.455(0.040) | RATCam
20130223 | 56346.20 | +21.7 |  $>$19.9 | 20.084(0.110) | 19.413(0.046) | 18.937(0.078) | 18.458(0.064) | RATCam
20130225 | 56348.14 | +23.6 |  $>$19.9 | 20.188(0.178) | 19.385(0.082) | 19.001(0.088) | 18.550(0.075) | RATCam
20130227 | 56350.30 | +25.8 | – | 20.226(0.124) | 19.510(0.093) | – | – | ANDICAM-CCD
20130301 | 56352.32 | +27.8 | – | – | – | 19.111(0.071) | 18.695(0.087) | ANDICAM-CCD
20130305 | 56356.25 | +31.8 | – | – | – | 19.113(0.054) | – | EFOSC2b
20130305 | 56356.26 | +31.8 | – | 20.367(0.077) | 19.616(0.056) | 19.167(0.045) | 18.558(0.065) | ANDICAM-CCD
20130310 | 56361.22 | +36.7 | – |  $>$20.4 |  $>$19.6 | 19.115(0.226) | 18.496(0.293) | RATCam
20130311 | 56362.26 | +37.8 | – | 20.509(0.052) | 19.618(0.052) | 19.076(0.050) | 18.594(0.063) | ANDICAM-CCD
20130312 | 56363.09 | +38.6 |  $>$19.9 | 20.590(0.080) | 19.688(0.051) | 19.143(0.054) | 18.625(0.051) | RATCam
20130315 | 56366.28 | +41.8 | – | 20.689(0.051) | 19.857(0.057) | 19.082(0.038) | 18.755(0.043) | ANDICAM-CCD
20130318 | 56369.07 | +44.6 |  $>$20.0 | 20.850(0.138) | 19.802(0.071) | 19.284(0.075) | 18.675(0.090) | RATCam
20130320 | 56371.33 | +46.8 | – | 20.949(0.060) | 19.984(0.063) | 19.257(0.030) | 18.735(0.084) | ANDICAM-CCD
20130321 | 56372.11 | +47.6 |  $>$20.1 | 20.921(0.088) | 19.991(0.049) | 19.295(0.067) | 18.721(0.057) | RATCam
20130324 | 56375.29 | +50.8 | – | 21.018(0.120) | 20.111(0.094) | 19.484(0.056) | 18.634(0.071) | ANDICAM-CCD
20130328 | 56379.26 | +54.8 | – | 21.277(0.358) | 19.913(0.131) | 19.469(0.159) | 18.610(0.125) | ANDICAM-CCD
20130401 | 56383.12 | +58.6 | – |  $>$21.2 | 20.089(0.195) | 19.386(0.202) | 18.656(0.130) | RATCam
20130407 | 56389.07 | +64.6 | – | 21.584(0.195) | 20.280(0.083) | 19.682(0.085) | 19.049(0.059) | RATCam
20130409 | 56392.00 | +67.5 | – | 21.746(0.225) | 20.476(0.097) | 19.863(0.104) | 18.963(0.102) | RATCam
20130414 | 56396.30 | +71.8 | – | 21.839(0.028) | 20.794(0.046) | 20.054(0.037) | 19.391(0.063) | EFOSC2
20150214 | 57067.31 | +742.8 | – | – | – |  $>$19.8 | – | PROMPT35b

a Phases are relative to the $R$-band maximum light: MJD=56324.5.

b Unfiltered data reported to broad-band Johnson-Cousins $R$ magnitudes.

$1$ This limit was obtained by L. Elenin (Lyubertsy, Russia) and I. Molotov
(Moscow, Russia) through a 0.45-m f/2.8 telescope plus KAF09000 CCD, which is
also reported in the Central Bureau for Astronomical Telegrams (CBAT, see
http://www.cbat.eps.harvard.edu/unconf/followups/J15213475-0722183.html).

Table 14: NIR ($JHK$) photometric measurements of AT 2013lb.

Date | MJD | Phasea |  $J$(err) |  $H$(err) |  $K$(err) | Instrument
---|---|---|---|---|---|---
20130208 | 56331.29 | +6.8 | 17.700(0.038) | 17.239(0.039) | 16.761(0.047) | SOFI
20130218 | 56341.30 | +16.8 | 17.967(0.165) | – | – | ANDICAM-IR
20130220 | 56343.29 | +18.8 | 17.988(0.184) | – | – | ANDICAM-IR
20130222 | 56345.36 | +20.9 | 17.977(0.096) | 17.339(0.039) | 16.975(0.052) | SOFI
20130227 | 56350.29 | +25.8 | 17.947(0.161) | – | – | ANDICAM-IR
20130301 | 56352.30 | +27.8 | 17.936(0.179) | – | – | ANDICAM-IR
20130305 | 56356.25 | +31.8 | 18.036(0.145) | – | – | ANDICAM-IR
20130306 | 56357.31 | +32.8 | 18.002(0.096) | 17.505(0.101) | 16.981(0.060) | SOFI
20130311 | 56362.25 | +37.8 | 18.137(0.205) | – | – | ANDICAM-IR
20130315 | 56366.27 | +41.8 | 18.070(0.135) | – | – | ANDICAM-IR
20130320 | 56371.32 | +46.8 | 18.004(0.153) | – | – | ANDICAM-IR
20130324 | 56375.27 | +50.8 | 18.068(0.136) | – | – | ANDICAM-IR
20130328 | 56379.25 | +54.8 | 18.182(0.215) | – | – | ANDICAM-IR
20130412 | 56394.33 | +69.8 | 18.292(0.081) | 17.705(0.067) | 17.362(0.065) | SOFI

a Phases are relative to the $R$-band maximum light: MJD=56324.5.

Table 15: Optical ($BVugriz$) photometric measurements of AT 2013la.

Date | MJD | Phasea |  $B$(err) |  $V$(err) |  $u$(err) |  $g$(err) |  $r$(err)b |  $i$(err)b | Instrument
---|---|---|---|---|---|---|---|---|---
20130331 | 56382.71 | -269.3 | – | – | – | – |  $>$18.8 | – | QHY9c
20131220 | 56646.93 | -5.4 | – | – | – | – | 18.246(0.251) | – | QHY9c
20131226 | 56652.96 | +1.0 | – | – | – | – | 17.992(0.230) | – | QHY9c
20131227 | 56653.93 | +1.9 | – | – | – | – | 17.964(0.180) | – | QHY9c
20131229 | 56655.87 | +3.9 | – | – | – | – | 18.062(0.165) | – | QHY9c
20131230 | 56656.87 | +4.9 | – | – | – | – |  $>$17.8 | – | QHY9c
20140101 | 56658.21 | +6.2 | 19.393(0.035) | 18.634(0.013) | 20.840(0.186) | – | 18.314(0.011) | 18.101(0.010) | IO:O
20140102 | 56659.16 | +7.2 | 19.386(0.045) | 18.691(0.030) | 20.519(0.218) | – | 18.351(0.015) | 18.133(0.016) | IO:O
20140104 | 56661.26 | +9.3 | 19.373(0.045) | 18.702(0.014) | 20.227(0.136) | – | 18.360(0.013) | 18.202(0.012) | IO:O
20140107 | 56664.26 | +12.3 | 19.522(0.034) | 18.763(0.051) | 20.160(0.108) | – | 18.490(0.039) | 18.293(0.121) | IO:O
20140107 | 56664.84 | +12.8 | – | – | – | – | 18.467(0.396) | – | QHY9c
20140108 | 56665.16 | +13.2 | 19.432(0.112) | 18.774(0.055) |  $>$19.6 | – | 18.511(0.069) | 18.208(0.044) | IO:O
20140108 | 56665.23 | +13.2 | – | 18.811(0.180) | – | – | 18.417(0.218) | – | AFOSC
20140109 | 56666.96 | +15.0 | – | – | – | – | 18.501(0.224) | – | QHY9c
20140111 | 56668.88 | +16.9 | – | – | – | – | 18.529(0.213) | – | QHY9c
20140115 | 56672.15 | +21.1 | 19.559(0.066) | 18.888(0.073) | 20.093(0.211) | – | 18.555(0.028) | 18.404(0.022) | IO:O
20140122 | 56679.14 | +27.1 | 19.650(0.085) | 19.083(0.058) | – | – | 18.636(0.256) | 18.672(0.058) | SBIG
20140127 | 56684.27 | +32.3 | 19.957(0.042) | 19.154(0.026) | – | – | 18.803(0.022) | 18.751(0.028) | IO:O
20140204 | 56692.23 | +40.2 | – | – | – | – | 19.111(0.008) | – | LRS
20140207 | 56695.24 | +43.2 | 20.223(0.037) | 19.357(0.022) | 20.386(0.186) | – | 19.030(0.019) | 18.985(0.023) | IO:O
20140209 | 56697.61 | +45.6 | – | – | – | 20.06 | – | – | 1
20140209 | 56697.62 | +45.6 | – | – | – | 20.13 | – | – | 1d
20140210 | 56698.24 | +46.2 | 20.187(0.038) | 19.480(0.032) | 20.485(0.150) | – | 19.037(0.018) | 19.002(0.027) | IO:O
20140213 | 56701.10 | +49.1 | 20.213(0.093) | 19.556(0.050) | – | – | 19.054(0.037) | 19.086(0.033) | IO:O
20140221 | 56709.60 | +57.6 | – | – | – | – | 19.14 | – | 1
20140221 | 56709.61 | +57.6 | – | – | – | – | 19.22 | – | 1
20140223 | 56711.22 | +59.2 | 20.350(0.051) | 19.607(0.029) | – | – | 19.205(0.022) | 19.244(0.027) | IO:O
20140226 | 56714.28 | +62.3 | – | – | – | – | 19.263(0.017) | 19.258(0.038) | OSIRIS
20140228 | 56716.19 | +64.2 | 20.550(0.054) | 19.653(0.033) |  $>$20.6 | – | 19.277(0.022) | 19.306(0.039) | IO:O
20140309 | 56725.17 | +73.2 | 20.603(0.238) | 19.923(0.104) | – | – | 19.535(0.104) | 19.389(0.049) | AFOSC
20140323 | 56739.10 | +87.1 | 21.051(0.038) | 20.250(0.061) | – | – | 19.644(0.008) | 19.781(0.010) | LRS
20140401 | 56748.08 | +96.1 | 21.267(0.158) | 20.291(0.219) | – | – | – | 19.934(0.032) | AFOSC
20140425 | 56772.99 | +121.0 | – | 20.697(0.023) | – | – | 19.838(0.012) | 20.107(0.019) | ALFOSC
20140428 | 56775.94 | +123.9 | – | – | – | – | 19.849(0.080) | 20.173(0.085) | OSIRIS
20140514 | 56791.93 | +139.9 | – | 20.985(0.086) | – | – | 19.927(0.039) | 20.357(0.064) | LRS
20140615 | 56823.94 | +171.9 | 21.713(0.048) | 21.340(0.033) | – | – | 20.151(0.015) | 20.545(0.017) | LRS
20140723 | 56861.92 | +209.9 | 21.949(0.054) | 21.454(0.035) | – | – | 20.310(0.013) | 20.619(0.023) | LRS
20140808 | 56877.88 | +225.9 | 22.257(0.070) | 21.693(0.047) | – | – | 20.447(0.020) | 20.816(0.025) | LRS
20140814 | 56883.88 | +231.9 | – | – | – | – | 20.540(0.165) | 20.925(0.046) | OSIRIS
20141217 | 57008.20 | +356.2 | – | – | – | – | 21.531(0.106) | – | ALFOSC
20141220 | 57011.19 | +359.2 | – | 22.302(0.539) | – | – | 21.406(0.106) | 21.540(0.196) | AFOSC
20141223 | 57014.25 | +362.2 | – | – | – | – | 21.450(0.168) | 21.612(0.124) | OSIRIS
20150125 | 57047.27 | +395.3 | – |  $>$22.5 | – | – | 21.815(0.034) | 21.967(0.041) | ALFOSC
20150311 | 57092.27 | +440.3 | – |  $>$22.6 | – | – | 22.436(0.070) | – | ALFOSC
20150428 | 57140.77 | +488.8 | – | – | – | – |  $>$23.0 | – | ALFOSC

a Phases are relative to the $r$-band maximum light: MJD=56652.0.

b Johnson-Cousins $R$ and $I$ filter data were transformed to Sloan $r$ and
$i$ band magnitudes respectively, following the relations of Jordi et al.
(2006)

c Measurements on unfiltered images, calibrated to the Sloan $r$-band
magnitudes.

d This epoch also has a $z$-band detection at 18.69 $\mathrm{mag}$. In
addition, there is a very early (2013-03-07; MJD=56476.29) $z$-band limit of
$>$ 20.8 mag.

$1$ These data were taken from the Pan-STARRS Survey for Transients (see
website:

https://star.pst.qub.ac.uk/ps1threepi/psdb/candidate/1131007351341051000/).

Table 16: Optical ($BVgriz$) photometric measurements of AT 2018aes.

Date | MJD | Phasea |  $B$(err) |  $V$(err) |  $g$(err) |  $r$(err) |  $i$(err) |  $z$(err) | Instrument
---|---|---|---|---|---|---|---|---|---
20180215 | 58164.65 | -46.5 | – | – | – |  $>$20.1 | – | – | ATLAS∗
20180218 | 58167.57 | -43.5 | – | – | – |  $>$18.7 | – | – | 1
20180307 | 58184.61 | -26.5 | – | – | – |  $>$20.1 | – | – | ATLAS
20180311 | 58188.54 | -22.6 | – | – | – | 18.51(0.3) | – | – | 1
20180311 | 58188.55 | -22.6 | – | – | – | – | 19.103(0.029) | – | 2
20180311 | 58188.61 | -22.5 | – | – | – | 19.21(0.60) | – | – | ATLAS
20180314 | 58191.73 | -19.4 | 20.004(0.089) | 19.321(0.084) | 19.613(0.054) | 19.051(0.061) | 18.881(0.103) | – | fl12
20180317 | 58194.59 | -16.5 | – | – | 19.52(0.44) | – | – | – | ATLAS
20180318 | 58195.09 | -16.0 | 19.794(0.074) | 19.185(0.084) | 19.558(0.021) | 18.997(0.052) | 18.727(0.080) | – | fl06
20180319 | 58196.59 | -14.5 | – | – | – | 18.78(0.34) | – | – | ATLAS
20180322 | 58199.12 | -12.0 | 19.841(0.027) | 19.140(0.020) | 19.509(0.011) | 18.949(0.023) | 18.896(0.023) | – | ALFOSC
20180322 | 58199.38 | -11.7 | 19.868(0.131) | 19.082(0.078) | 19.402(0.047) | 18.919(0.061) | 18.775(0.080) | – | fl05
20180326 | 58203.23 | -7.9 |  $>$19.6 | 18.904(0.064) | 19.314(0.045) | 18.830(0.048) | 18.663(0.072) | – | fl03
20180329 | 58206.50 | -4.6 | – | – | – | 18.84(0.31) | – | – | ATLAS
20180330 | 58207.11 | -4.0 | 19.714(0.068) | 19.089(0.065) | 19.383(0.064) | 18.827(0.045) | 18.716(0.041) | 18.634(0.075) | ALFOSC
20180405 | 58213.09 | +2.0 | 19.830(0.020) | 19.019(0.010) | 19.386(0.010) | 18.858(0.010) | 18.546(0.049) | 18.569(0.027) | ALFOSC
20180407 | 58215.19 | +4.1 | – | 19.069(0.026) | 19.465(0.031) | 18.750(0.050) | 18.575(0.027) | 18.479(0.045) | ALFOSC
20180408 | 58216.16 | +5.1 | 19.923(0.029) | 19.068(0.019) | 19.486(0.010) | 18.871(0.015) | 18.652(0.025) | 18.605(0.041) | ALFOSC
20180411 | 58219.14 | +8.0 | 19.934(0.025) | 19.011(0.011) | 19.559(0.010) | 18.876(0.019) | 18.632(0.030) | 18.596(0.035) | ALFOSC
20180412 | 58220.53 | +9.4 | – | – | – | 18.77(0.10) | – | – | ATLAS
20180417 | 58225.03 | +13.9 | 20.104(0.042) | 19.220(0.024) | 19.590(0.025) | 18.952(0.024) | 18.725(0.018) | 18.574(0.037) | ALFOSC
20180418 | 58226.10 | +15.0 | 20.184(0.075) | 19.224(0.029) | 19.653(0.018) | 19.021(0.022) | 18.773(0.040) | 18.758(0.051) | IO:O
20180418 | 58226.98 | +15.9 | – | 19.138(0.104) | 19.648(0.094) | 19.039(0.078) | 19.005(0.135) | – | Moravian
20180419 | 58227.98 | +16.9 | 20.121(0.175) | 19.205(0.088) | 19.736(0.090) | 18.969(0.099) | 18.811(0.219) | – | Moravian
20180426 | 58234.13 | +23.0 | 20.389(0.033) | 19.563(0.017) | 19.885(0.025) | 19.172(0.021) | 18.899(0.038) | 18.785(0.043) | ALFOSC
20180501 | 58239.04 | +27.9 | 20.584(0.049) | 19.570(0.022) | 20.099(0.019) | 19.390(0.043) | 19.089(0.032) | 19.033(0.046) | ALFOSC
20180504 | 58242.98 | +31.9 | 20.771(0.134) | 19.654(0.050) | 20.124(0.054) | 19.476(0.031) | 19.200(0.050) | 18.999(0.078) | IO:O
20180507 | 58245.98 | +34.9 | 20.820(0.104) | 19.781(0.028) | 20.478(0.033) | 19.538(0.013) | 19.313(0.061) | 19.021(0.090) | IO:O
20180510 | 58248.48 | +37.4 | – | – | – | 19.66(0.62) | – | – | ATLAS
20180513 | 58251.02 | +39.9 | 21.111(0.146) | 20.175(0.043) | 20.566(0.065) | 19.798(0.041) | 19.568(0.082) | 19.145(0.068) | IO:O
20180515 | 58254.00 | +42.9 | 21.182(0.086) | 20.189(0.041) | 20.693(0.041) | 19.938(0.036) | 19.473(0.037) | 19.181(0.044) | ALFOSC
20180517 | 58255.95 | +44.8 | 21.239(0.210) | 20.276(0.080) | 20.972(0.051) | 20.008(0.039) | 19.651(0.121) | 19.313(0.070) | IO:O
20180522 | 58260.92 | +49.8 |  $>$21.2 | 20.468(0.120) | 21.261(0.373) | 20.140(0.087) | 19.985(0.116) | 19.498(0.118) | IO:O
20180525 | 58263.05 | +52.0 | 21.714(0.111) | 20.559(0.105) | 21.343(0.046) | 20.356(0.071) | 20.092(0.082) | 19.728(0.071) | ALFOSC
20180531 | 58269.02 | +57.9 | 22.048(0.164) | 20.986(0.060) | 21.813(0.062) | 20.608(0.024) | 20.257(0.121) | 19.910(0.093) | ALFOSC
20180531 | 58269.94 | +58.8 |  $>$21.8 |  $>$20.9 |  $>$21.6 |  $>$20.7 | 20.332(0.275) | 19.900(0.267) | IO:O
20180605 | 58274.05 | +62.9 | 22.189(0.128) | 21.106(0.070) | 21.898(0.073) | 20.907(0.032) | 20.567(0.114) | 19.917(0.060) | ALFOSC
20180605 | 58274.91 | +63.8 |  $>$21.8 | 21.280(0.075) | 21.956(0.120) | 20.831(0.044) | 20.708(0.435) | 19.911(0.161) | IO:O
20180610 | 58279.99 | +68.9 |  $>$21.8 | 21.454(0.193) | 22.124(0.147) | 21.304(0.123) | 20.712(0.258) | 20.258(0.235) | IO:O
20180626 | 58295.97 | +84.9 | – | – |  $>$22.5 | 22.335(0.104) |  $>$21.8 | 20.996(0.226) | ALFOSC
20180704 | 58303.97 | +92.9 | – | – | – | 22.865(0.221) | 21.866(0.379) | 21.414(0.211) | ALFOSC

a Phases are relative to the $r$-band maximum light: MJD= 58211.1.

∗ ATLAS (Asteroid Terrestrial-impact Last Alert System; Heinze et al. 2018;
Tonry et al. 2018; Smith et al. 2020) observations in cyan\- and orange-band
magnitudes are reported in the sloan g and r columns respectively.

$1$ Unfiltered KAIT data reported to the sloan $r$ magnitudes (AB system).
Data from the Transient Name Server (TNS; https://wis-
tns.weizmann.ac.il/object/2018aes).

$2$ The $i$-band magnitude is the weighted mean value obtained from the Pan-
STARRS Survey for Transients (see website:
https://star.pst.qub.ac.uk/sne/ps13pi/psdb/lightcurve/1134817771035644300/).

Table 17: NIR ($JHK$) photometric measurements of AT 2018aes.

Date | MJD | Phasea |  $J$(err) |  $H$(err) |  $K$(err) | Instrument
---|---|---|---|---|---|---
20180331 | 58209.00 | -2.1 | 17.781(0.040) | 17.387(0.075) | 16.235(0.088) | NOTCam
20180511 | 58249.92 | +38.8 | 18.257(0.065) | 17.994(0.063) | 17.148(0.076) | NOTCam
20180627 | 58296.95 | +85.9 | 19.752(0.209) | 19.363(0.299) | 17.957(0.160) | NOTCam
20180731 | 58330.88 | +119.8 |  $>$ 20.5 | 19.662(0.392) | – | NOTCam
20180819 | 58349.86 | +138.8 | – | – | 18.442(0.186) | NOTCam

a Phases are relative to the $r$-band maximum light: MJD= 58211.1.