Brief Review — Rubik’s Cube+: A self-supervised feature learning framework for 3D medical image analysis

Self-Supervised Learning by Playing Rubik’s Cube

  • A pretext task, Rubik’s Cube+, is proposed, which involves three operations, namely cube ordering, cube rotating and cube masking.
  • Compared to Rubik’s Cube, cube masking is added for the pretext task.


  1. Rubik’s Cube+
  2. Results

1. Rubik’s Cube+

Rubik’s Cube+ Framework

1.1. Network Architecture

  • A 3D medical volume is first partitioned it into a grid (e.g., 2×2×2) of cubes, and then permuted with random rotations, as well as masking.
  • The cube intensities are normalized to [−1, 1].
  • A Siamese network with M (which is the number of cubes) sharing weight branches, namely Siamese-Octad, is adopted to solve Rubik’s cube.
  • 3D CNN, e.g., 3D ResNet & 3D VGG are used.
  • The feature maps from the last fully-connected or convolution layer of all branches are concatenated and given as input to the fully-connected layer of separate tasks, i.e., cube ordering and orientating, which are supervised by permutation loss (LP) and rotation loss (LR), respectively.

1.2. Permutation Loss

  • Same as the one in Rubik’s Cube, the network needs to predict the permutation from the K options, which can be seen as a classification task with K categories. The corresponding loss is:

1.3. Rotation Loss

  • Same as the one in Rubik’s Cube. The directions for cube rotation are limited, i.e., only allowing 180◦ horizontal and vertical rotations. The network is required to recognize whether each of the input cubes has been rotated. The predictions of this task are two 1×M vectors (r) indicating the possibilities of horizontal (hor) and vertical (ver) rotations for each cube. The corresponding loss is:

1.4. Masking Loss

  • The process of random masking strategy can be summarized as:
  1. First, a random possibility (pos ∈ [0, 1]) is generated for each cube to determine whether it should be masked or not.
  2. If the cube is to be masked (i.e., pos≥0.5), we generate a 3D matrix R of the same shape of a cube to randomly block the content. The value of each voxel of R is a probability (prob) randomly captured from a uniform distribution [0, 1].
  3. To obtain the mask, a thresholding operation ( th_R=0.5 ) is performed to R, which leads the voxel value of (x, y, z) to be 1 for prob(x, y, z)≥th_R and 0 versa vice.
  • The mask identification as a multi-label classification task, which is similar to cube orientation. Let gb represent a 1 ×M ground truth for cube masking, where 1 on the position of masked cubes and 0 vice versa, and b is the M prediction.
  • Then, the masking identification loss (LM) can be defined as:

1.5. Full Objectives

  • The total loss is the sum of LP, LR & LM:
  • where the loss weighting ratio is 1:1:1 indeed.

2. Results

2.1. Target Task: Classification

The average classification accuracy (ACC %) and the area under curve (AUC) of 3D networks trained with different strategies on the validation set of cerebral hemorrhage dataset
  • Due to the gap between natural video and volumetric medical data, the improvement yielded by UCF101 pre-trained weights is limited.

2.2. Target Task: Segmentation

The segmentation accuracy of different approaches on the BraTS-2018 validation set
Visualization of brain tumor segmentation results
  • Green, yellow and red stand for the whole tumor, tumor core and enhancing tumor
  • Compared to train-from-scratch, the L-U-Net pre-trained on Rubik’s cube+ pretext task produces more plausible segmentation results, especially for the tumor core and enhancing tumor.


[2020 JMIA] [Rubik’s Cube+]
Rubik’s Cube+: A self-supervised feature learning framework for 3D medical image analysis

Self-Supervised Learning

19932020 … [Rubik’s Cube+] 2021 [MoCo v3] [SimSiam] [DINO] [Exemplar-v1, Exemplar-v2] [MICLe] [Barlow Twins]

Biomedical Image Classification

2019 [CheXpert] [Rubik’s Cube] 2020 [VGGNet for COVID-19] [Dermatology] [Rubik’s Cube+] 2021 [MICLe]

Biomedical Image Segmentation

2015 … 2019 [DUNet] [NN-Fit] [Rubik’s Cube] 2020 [MultiResUNet] [UNet 3+] [Dense-Gated U-Net (DGNet)] [Rubik’s Cube+]

My Other Previous Paper Readings



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