Scale Equivariant Neural Networks with Morphological Scale-Spaces

Sangalli, Mateus; Blusseau, Samy; Velasco-Forero, Santiago; Angulo, Jesús

doi:10.1007/978-3-030-76657-3_35

Cited by 9 publications

(8 citation statements)

References 7 publications

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“…Unfortunately, no numeric values of the accuracies are provided, so we can compare the results only qualitatively. The Riesz network's accuracy varies less on a larger range of scales than those of the scale-equivariant networks on Gaussian or morphological scale spaces from [37] that were trained on scale 2. The Gaussian derivative network [27] trained on scale 1 yields results in a range between 98% and 99% for medium scales [0.7, 4.7] using pooling over 8 scales.…”

Section: Discussionmentioning

confidence: 98%

“…Further works considering the MNIST Large Scale data set are [27,37]. Unfortunately, no numeric values of the accuracies are provided, so we can compare the results only qualitatively.…”

Section: Discussionmentioning

confidence: 99%

“…Making use of the semi-group property of scale spaces, scale-equivariant neural networks motivate the use of dilated convolutions [35] to define scale-equivariant convolutions on the Gaussian scale space [36] or morphological scale spaces [37]. Unfortunately, these neural networks are unable to generalize to scales outside those determined by their architecture and are only suitable for downscale factors which are powers of 2, i.e., {2, 4, 8, 16, .…”

Section: Scale-invariant Deep Learning Methods For a Limited Range Of...mentioning

confidence: 99%

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Riesz Networks: Scale-Invariant Neural Networks in a Single Forward Pass

Barisin,

Schladitz,

Redenbach

2024

J Math Imaging Vis

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Scale invariance of an algorithm refers to its ability to treat objects equally independently of their size. For neural networks, scale invariance is typically achieved by data augmentation. However, when presented with a scale far outside the range covered by the training set, neural networks may fail to generalize. Here, we introduce the Riesz network, a novel scale- invariant neural network. Instead of standard 2d or 3d convolutions for combining spatial information, the Riesz network is based on the Riesz transform which is a scale-equivariant operation. As a consequence, this network naturally generalizes to unseen or even arbitrary scales in a single forward pass. As an application example, we consider detecting and segmenting cracks in tomographic images of concrete. In this context, ‘scale’ refers to the crack thickness which may vary strongly even within the same sample. To prove its scale invariance, the Riesz network is trained on one fixed crack width. We then validate its performance in segmenting simulated and real tomographic images featuring a wide range of crack widths. An additional experiment is carried out on the MNIST Large Scale data set.

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Section: Discussionmentioning

confidence: 98%

“…Further works considering the MNIST Large Scale data set are [27,37]. Unfortunately, no numeric values of the accuracies are provided, so we can compare the results only qualitatively.…”

Section: Discussionmentioning

confidence: 99%

Section: Scale-invariant Deep Learning Methods For a Limited Range Of...mentioning

confidence: 99%

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Riesz Networks: Scale-Invariant Neural Networks in a Single Forward Pass

Barisin,

Schladitz,

Redenbach

2024

J Math Imaging Vis

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“…The U-Net model is an improved and extended version of Fully Convolutional Networks (FCNs), designed as a semantic method. Its name originates from the "U" shape formed by its structure, and it was initially widely applied in the semantic segmentation of medical images [24,25]. As shown in Figure 4, the model consists of a contracting path on the left and an expansive path on the right.…”

Section: The U-net Modelmentioning

confidence: 99%

Recognition of Plastic Film in Terrain-Fragmented Areas Based on Drone Visible Light Images

Du,

Huang,

Dai

et al. 2024

Agriculture

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In order to meet the growing demand for food and achieve food security development goals, contemporary agriculture increasingly depends on plastic coverings such as agricultural plastic films. The remote sensing-based identification of these plastic films has gradually become a necessary tool for agricultural production management and soil pollution prevention. Addressing the challenges posed by the complex terrain and fragmented land parcels in karst mountainous regions, as well as the frequent presence of cloudy and foggy weather conditions, the extraction efficacy of mulching films is compromised. This study utilized a DJI Mavic 2 Pro UAV to capture visible light images in an area with complex terrain features such as peaks and valleys. A plastic film sample dataset was constructed, and the U-Net deep learning model parameters integrated into ArcGIS Pro were continuously modified and optimized to achieve precise plastic film identification. The results are as follows: (1) Sample quantity significantly affects recognition performance. When the sample size is 800, the accuracy of plastic film extraction notably improves, with area accuracy reaching 91%, a patch quantity accuracy of 96.38%, and an IOU and F1-score of 85.89% and 94.20%, respectively, compared to the precision achieved with a sample size of 300; (2) Different learning rates, batch sizes, and iteration numbers have a certain impact on the training effectiveness of the U-Net model. The most suitable model parameters improved the training effectiveness, with the highest training accuracy achieved at a learning rate of 0.001, a batch size of 10, and 25 iterations; (3) Comparative experiments with the Support Vector Machine (SVM) model validate the suitability of U-Net model parameters and sample datasets for precise identification in rugged terrains with fragmented spatial distribution, particularly in karst mountainous regions. This underscores the applicability of the U-Net model in recognizing plastic film coverings in karst mountainous regions, offering valuable insights for agricultural environmental health assessment and green planting management in farmlands.

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“…From the translation equivariance (and a form of linearity) it also follows that the architectures that employ scalespaces are naturally convolution neural networks, which are easy to implement and fast to evaluate due to the highly parallelizable nature of convolutional operations. In recent scale equivariant networks literature [18][19][20][21] the link to scale-space theory is also emphasized. In fact, the architectures they design are scale-spaces in the broad sense.…”

Section: Introductionmentioning

confidence: 99%

PDE-CNNs: Axiomatic Derivations and Applications

Bellaard,

Sakata,

Smets

et al. 2024

Preprint

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PDE-based Group Convolutional Neural Networks (PDE-G-CNNs) utilize solvers of geometrically meaningful evolution PDEs as substitutes for the conventional components in G-CNNs. PDE-G-CNNs offer several key benefits all at once: fewer parameters, inherent equivariance, better performance, data efficiency, and geometric interpretability. In this article we focus on Euclidean equivariant PDE-G-CNNs where the feature maps are two dimensional throughout. We call this variant of the framework a PDE-CNN. From a machine learning perspective, we list several practically desirable axioms and derive from these which PDEs should be used in a PDE-CNN. Here our approach to geometric learning via PDEs is inspired by the axioms of classical linear and morphological scale-space theory, which we generalize by introducing semifield-valued signals. Furthermore, we experimentally confirm for small networks that PDE-CNNs offer fewer parameters, increased performance, and better data efficiency when compared to CNNs. We also investigate what effect the use of different semifields has on the performance of the models.

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Scale Equivariant Neural Networks with Morphological Scale-Spaces

Cited by 9 publications

References 7 publications

Riesz Networks: Scale-Invariant Neural Networks in a Single Forward Pass

Riesz Networks: Scale-Invariant Neural Networks in a Single Forward Pass

Recognition of Plastic Film in Terrain-Fragmented Areas Based on Drone Visible Light Images

PDE-CNNs: Axiomatic Derivations and Applications

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