Network Receptive Field Research Articles

CPAD-Net: Contextual parallel attention and dilated network for liver tumor segmentation

Liver cancer is one of the leading causes of cancer death. Accurate and automatic liver tumor segmentation methods are urgent needs in clinical practice. Currently, Fully Convolutional Network and U-Net framework have achieved good results in medical image segmentation tasks, but there is still room for improvement. The traditional U-Net extracted a large number of low-level features, and the detailed features cannot be transmitted to deeper layers, resulting in poor segmentation ability. Therefore, this paper proposed a novel liver tumor segmentation network with contextual parallel attention and dilated convolution, called CPAD-Net. The proposed network applies a subsampled module, which has the same dimensionality reduction function as max-pooling without losing detailed features. CPAD-Net employs a contextual parallel attention module at skip connection. The module fuses contextual multi-scale features and extracts channel-spatial features in parallel. These features are concatenated with deep features to narrow the semantic gap and increase detailed information. Hybrid dilated convolution and double-dilated convolution are used in the encoding and decoding stages to expand the network receptive field. Dropout is added after each hybrid dilated convolution block to prevent overfitting. The efficacy of the proposed network is proved by widespread experimentation on two public datasets (LiTS2017 and 3Dircadb-01) and a clinical dataset from the Affiliated Hospital of Hebei University. The proposed network achieved Dice scores of 74.2%, 73.7% and 73.26%. The experimental results show that the proposed network outperforms most segmentation networks.

River Extraction from Remote Sensing Images in Cold and Arid Regions Based on Attention Mechanism

The extraction of rivers in cold and arid regions is of great significance for applications such as ecological environment monitoring, agricultural planning, and disaster warning. However, there are few related studies on river extraction in cold and arid regions, and it is still in its infancy. The accuracy of river extraction is low, and the details are blurred. The rapid development of deep learning has provided us with new ideas, but with lack of corresponding professional datasets, the accuracy of the current semantic segmentation network is not high. This study mainly presents the following. (1) According to the characteristics of cold and arid regions, a professional dataset was made to support the extraction of rivers from remote sensing images in these regions. (2) Combine transfer learning and deep learning, migrate the ResNet-101 network to the LinkNet network, and introduce the attention mechanism to obtain the AR-LinkNet network, which is used to improve the recognition accuracy of the network. (3) A channel attention module and a spatial attention module with residual structure are proposed to strengthen the effective features and improve the segmentation accuracy. (4) Combining dense atrous spatial pyramid pooling (DenseASPP) with AR-LinkNet network expands the network receptive field, which can extract more detailed information and increase the coherence of extracted rivers. (5) For the first time, the binary cross-entropy loss function combined with the Dice loss function is applied to river extraction as a new loss function, which accelerates the network convergence and improves the image quality. Validation on the dataset shows that, compared with typical semantic segmentation networks, the method performs better on evaluation metrics such as recall, intersection ratio, precision, and F 1 score, and the extracted rivers are clearer and more coherent.

Tooth instance segmentation based on capturing dependencies and receptive field adjustment in cone beam computed tomography

AbstractAutomatic and accurate instance segmentation of teeth can provide important support for computer‐aided orthodontic work. Traditional methods for tooth segmentation studies often ignore the rich structural features of teeth. Capturing the complete and accurate geometry as well as morphological details of a single tooth remains a challenge for current tooth segmentation studies. In this article, a new tooth segmentation deeplearning network based on capturing dependencies and receptive field adjustment in cone beam computed tomography (CBCT) is proposed to achieve automatic and accurate instance segmentation of dental CBCT data. The method acquires coarse‐level features of tooth and accurate tooth centroids in the first stage, and acquires the instance information and spatial position localization of the tooth. The encoding process in the second stage of the network introduces a guidance module for obtaining tooth geometry information based on a 3D self‐attention mechanism to capture dependencies in CBCT. The proposed tooth feature integration module is based on multiscale fusion of dilated convolutions to capture tooth detailed information at multiple scales, and the network receptive field was adjusted. Extensive evaluation, ablation, and comparison experiments demonstrate that our method exhibits state‐of‐the‐art segmentation performance and accurate instance segmentation results, reflecting their potential applicability in clinical medicine.

A regularization‐based deep unsupervised model for affine multimodal co‐registration

AbstractExtensive network receptive field is key for unsupervised affine registration because instead of deformable registration that takes care of local subtleties, the affine registration is global so that the last layers need to see big patches of the organ‐in‐interest. To extend the network's receptive field, we need to go for deeper networks, which causes producing complex models. On the other hand, affine transformation is restricted by its low degree‐of‐freedom (DoF) where larger models increasingly develop the hazard of overfitting. To worsen the situation, the regularizer module cannot be applied to the affine transformation with such a restricted DoF. In this paper, we propose a differentiable computational layer to convert the affine transformation outputted by the network to its corresponding dense displacement field. Such an affine‐to‐field layer enables us to apply different regularization terms on the outputted transformation in order to avoid the overfitting phenomenon while deepening the network. The proposed approach was evaluated on an annotated hard multimodal dataset containing 1109 pairs of CT/MR images of the brain with different heterogeneity for example, variety in scanners, setups and resolutions. Based on the results, the proposed customized layer is fully successful to handle the overfitting for deeper networks that are able to produce richer transformations than the shallower networks from different evaluation metrics for example, in target registration error the proposed network with seven layers has a 13.3% (or 9.1 mm) improvement in performance. The implementation of the proposed customized affine‐to‐field layer in the Python, Keras package with the Tensorflow backend can be publically accessed via https://github.com/boveiri/Deep-coReg.

HLNet Model and Application in Crop Leaf Diseases Identification

Crop disease has been a severe issue for agriculture, causing economic loss for growers. Thus, disease identification urgently needs to be addressed, especially for precision agriculture. As of today, deep learning has been widely used for crop disease identification combined with optical imaging sensors. In this study, a lightweight convolutional neural network model is designed and validated on two publicly available imaging datasets and one self-built dataset with 28 types of leaf and leaf disease images of 6 crops as the research object. This model is an improvement of the existing convolutional neural network, reducing the floating-point operations by 65%. In addition, dilated depth-wise convolutions were used to increase the network receptive field and improve the model recognition accuracy without affecting the network computational speed. Meanwhile, two attention mechanisms are optimized to reduce attention module computation, improving the capability of the model to select the correct regions of interest. After training, this model achieved an average accuracy of 99.86%, and the image calculation speed was 0.173 s. Comparing with 11 backbone models and 5 latest crop leaf disease identification studies, the proposed model achieved the highest accuracy. Therefore, this model with an advantage of balancing between the calculation speed and recognition accuracy. Furthermore, the proposed model provides a theoretical basis and technical support for the practical application and mobile terminal applications of crop disease recognition in precision agriculture.

Metallic debossed characters industrial online non‐segmentation identification based on improved multi‐scale image fusion enhancement and deep neural network

This paper investigates accurate industry online scene text recognition techniques for metallic debossed characters (MDCs). As MDCs have low contrast with its background and easy to interfere with corrosion rust, oxidate skin or specular reflection and so forth, a multi-scale image fusion algorithm is first proposed to restore the MDCs’ shape and appearance information to enhance the sample's contrast by using the MDCs' depth characteristic with the help of four-directional illumination. With this method, the three most important reflection-related picture quality evaluation standards, namely contrast, saturation, and exposure, can be enhanced simultaneously. Next, based on the fusion result, a U-shaped network based on VGG-16 network architecture is used for text localization. In order to improve network receptive fields, an improved post-processing output module that combines a text sequence score map for coarsening localization with a single-character score map for fine localization is proposed, so that the network's adaptability and accuracy for long texts are improved. Finally, a convolutional recurrent neural network is adopted to realize the recognition of sequence characters. The advantages and effectiveness of the proposed method are statistically analyzed with the data from a liquefied petroleum gas cylinder annual periodic inspection production line.

Multiscale residual fusion network for image denoising

Deep-learning methods have been developed in recent years and have achieved dramatic improvements for image denoising. The existing deep-learning methods can be conducted using two major models: Encoder–decoder and high-resolution, where the high-resolution model has superior resolution ability for detail description and restoration. In this study, a high-resolution-based network called multiscale residual fusion network (MRF-Net) is proposed, which employed the spatial and contextual information of images. In detail, dilated convolution layers are used to enlarge the network's receptive field and learned sufficient features in a multiscale feature extracting module. The function of dilated convolution is reinterpreted here and it is viewed as a complex downsampling operation. Therefore, multiscale feature analysis could be performed in the proposed network by dilated convolution. Multilevel feature maps are sequentially obtained through a residual projection module, where considerable contextual and spatial information was collected from the multiscale features. In a residual fusion module, all maps were aggregated to generate a residual image effectively for noise removal. Experiments demonstrated that the MRF-Net outperformed several state-of-the-art model-based and deep-learning methods in both blind and non-blind image denoising tests. Meanwhile, ablation studies were executed to verify the denoising performance of each module. Moreover, this method exhibited high computational efficiency, thus demonstrating its practicability.

Developing and Evaluating Deep Neural Network-Based Denoising for Nanoparticle TEM Images with Ultra-Low Signal-to-Noise

Abstract A deep convolutional neural network has been developed to denoise atomic-resolution transmission electron microscope image datasets of nanoparticles acquired using direct electron counting detectors, for applications where the image signal is severely limited by shot noise. The network was applied to a model system of CeO2-supported Pt nanoparticles. We leverage multislice image simulations to generate a large and flexible dataset for training the network. The proposed network outperforms state-of-the-art denoising methods on both simulated and experimental test data. Factors contributing to the performance are identified, including (a) the geometry of the images used during training and (b) the size of the network's receptive field. Through a gradient-based analysis, we investigate the mechanisms learned by the network to denoise experimental images. This shows that the network exploits both extended and local information in the noisy measurements, for example, by adapting its filtering approach when it encounters atomic-level defects at the nanoparticle surface. Extensive analysis has been done to characterize the network's ability to correctly predict the exact atomic structure at the nanoparticle surface. Finally, we develop an approach based on the log-likelihood ratio test that provides a quantitative measure of the agreement between the noisy observation and the atomic-level structure in the network-denoised image.

A temporal-spectral generative adversarial network based end-to-end packet loss concealment for wideband speech transmission.

Packet loss concealment (PLC) aims to mitigate speech impairments caused by packet losses so as to improve speech perceptual quality. This paper proposes an end-to-end PLC algorithm with a time-frequency hybrid generative adversarial network, which incorporates a dilated residual convolution and the integration of a time-domain discriminator and frequency-domain discriminator into a convolutional encoder-decoder architecture. The dilated residual convolution is employed to aggregate the short-term and long-term context information of lost speech frames through two network receptive fields with different dilation rates, and the integrated time-frequency discriminators are proposed to learn multi-resolution time-frequency features from correctly received speech frames with both time-domain waveform and frequency-domain complex spectrums. Both causal and noncausal strategies are proposed for the packet-loss problem, which can effectively reduce the transitional distortion caused by lost speech frames with a significantly reduced number of training parameters and computational complexity. The experimental results show that the proposed method can achieve better performance in terms of three objective measurements, including the signal-to-noise ratio, perceptual evaluation of speech quality, and short-time objective intelligibility. The results of the subjective listening test further confirm a better performance in the speech perceptual quality.

A hybrid deep convolutional neural network for accurate land cover classification

Land cover classification provides updated information regarding the Earth's resources, which is vital for agricultural investigation, urban management, and disaster monitoring. Current advances in sensor technology on satellite and aerial remote sensing (RS) devices have improved the spatial-spectral, radiometric, and temporal resolutions of images over time. These improvements offer invaluable chances of understanding land cover information. However, land cover classification from RS images is an intricate task because of the high intra-class disparities, low inter-class similarities, and image variation types. We propose a cascaded residual dilated network (CRD-Net) for land cover classification using very high spatial resolution (VHSR) images to address these challenges. The proposed hybrid network follows the encoder-decoder concept with a spatial attention block to guide the network on learnable discriminate features coupled with an intermediary loss to enhance the training process. Moreover, a cascaded residual dilated module increases the network's receptive field to enrich multi-contextual features further, thus boosting the resultant feature descriptor. Extensive experimental results demonstrate that the proposed CRD-Net outperformed state-of-the-art methods, achieving an overall accuracy (OA) of 90.73% and 90.51% on the ISPRS Potsdam land cover dataset and ISPRS Vaihingen dataset, respectively.

Exact Tile-Based Segmentation Inference for Images Larger than GPU Memory.

We address the problem of performing exact (tiling-error free) out-of-core semantic segmentation inference of arbitrarily large images using fully convolutional neural networks (FCN). FCN models have the property that once a model is trained, it can be applied on arbitrarily sized images, although it is still constrained by the available GPU memory. This work is motivated by overcoming the GPU memory size constraint without numerically impacting the final result. Our approach is to select a tile size that will fit into GPU memory with a halo border of half the network receptive field. Next, stride across the image by that tile size without the halo. The input tile halos will overlap, while the output tiles join exactly at the seams. Such an approach enables inference to be performed on whole slide microscopy images, such as those generated by a slide scanner. The novelty of this work is in documenting the formulas for determining tile size and stride and then validating them on U-Net and FC-DenseNet architectures. In addition, we quantify the errors due to tiling configurations which do not satisfy the constraints, and we explore the use of architecture effective receptive fields to estimate the tiling parameters.

Super-resolution infrared imaging via multi-receptive field information distillation network

We propose a super-resolution (SR) infrared imaging method with a multi-receptive field information distillation network. We develop a parallel progressive feature purification model to optimize the feature extraction progress and retain feature in each dimension. We use the dilation convolution to enlarge the network's receptive field and keep the number of parameters steady. We reconstruct a SR infrared image by a sub-pixel method. A series of experiments are implemented. The imaging performance of the proposed method is validated by comparing with the results from classical interpolate Bicubic, and deep learning methods VDSR, SRResNet and IMDN. Experimental results suggest that the proposed method performs favorably against the four state-of-the-art SR algorithms in visual quality. The proposed system can realize high quality image reconstruction and 2-scale SR, and requires much less images numbers for training.

MRENet: Simultaneous Extraction of Road Surface and Road Centerline in Complex Urban Scenes from Very High-Resolution Images

Automatic extraction of the road surface and road centerline from very high-resolution (VHR) remote sensing images has always been a challenging task in the field of feature extraction. Most existing road datasets are based on data with simple and clear backgrounds under ideal conditions, such as images derived from Google Earth. Therefore, the studies on road surface extraction and road centerline extraction under complex scenes are insufficient. Meanwhile, most existing efforts addressed these two tasks separately, without considering the possible joint extraction of road surface and centerline. With the introduction of multitask convolutional neural network models, it is possible to carry out these two tasks simultaneously by facilitating information sharing within a multitask deep learning model. In this study, we first design a challenging dataset using remote sensing images from the GF-2 satellite. The dataset contains complex road scenes with manually annotated images. We then propose a two-task and end-to-end convolution neural network, termed Multitask Road-related Extraction Network (MRENet), for road surface extraction and road centerline extraction. We take features extracted from the road as the condition of centerline extraction, and the information transmission and parameter sharing between the two tasks compensate for the potential problem of insufficient road centerline samples. In the network design, we use atrous convolutions and a pyramid scene parsing pooling module (PSP pooling), aiming to expand the network receptive field, integrate multilevel features, and obtain more abundant information. In addition, we use a weighted binary cross-entropy function to alleviate the background imbalance problem. Experimental results show that the proposed algorithm outperforms several comparative methods in the aspects of classification precision and visual interpretation.

Efficient Attention Fusion Network in Wavelet Domain for Demoireing

When taking pictures of electronic screens or objects with high-frequency textures, people often run across colorful rainbow patterns that are known as “moire”, seriously affecting the image quality and subsequent processing. Current methods for removing moire patterns mostly extract multiscale information by downsampling pooling layers, which may inevitably cause information loss. To address this issue, this paper proposes a demoireing method in the wavelet domain. By employing both discrete wavelet transform (DWT) and inverse discrete wavelet transform (IDWT) instead of traditional downsampling and upsampling, this method can effectively increase the network receptive field without information loss. In addition, to further reconstruct more details of moire patterns, this paper proposes an efficient attention fusion module (EAFM). With a combination of efficient channel attention, spatial attention and local residual learning, this module can self-adaptively learn various weights of feature information at different levels and inspire the network to focus more on effective information such as moire details to improve learning and demoireing performance. Extensive experiments based on public datasets have shown that this suggested method can efficiently remove moire patterns and has a good quantitative and qualitative performance.

Esophageal Tumor Segmentation in CT Images Using a Dilated Dense Attention Unet (DDAUnet)

Manual or automatic delineation of the esophageal tumor in CT images is known to be very challenging. This is due to the low contrast between the tumor and adjacent tissues, the anatomical variation of the esophagus, as well as the occasional presence of foreign bodies (e.g. feeding tubes). Physicians therefore usually exploit additional knowledge such as endoscopic findings, clinical history, additional imaging modalities like PET scans. Achieving his additional information is time-consuming, while the results are error-prone and might lead to non-deterministic results. In this paper we aim to investigate if and to what extent a simplified clinical workflow based on CT alone, allows one to automatically segment the esophageal tumor with sufficient quality. For this purpose, we present a fully automatic end-to-end esophageal tumor segmentation method based on convolutional neural networks (CNNs). The proposed network, called Dilated Dense Attention Unet (DDAUnet), leverages spatial and channel attention gates in each dense block to selectively concentrate on determinant feature maps and regions. Dilated convolutional layers are used to manage GPU memory and increase the network receptive field. We collected a dataset of 792 scans from 288 distinct patients including varying anatomies with air pockets, feeding tubes and proximal tumors. Repeatability and reproducibility studies were conducted for three distinct splits of training and validation sets. The proposed network achieved a DSC value of 0.79 ± 0.20, a mean surface distance of 5.4 ± 20.2mm and 95% Hausdorff distance of 14.7 ± 25.0mm for 287 test scans, demonstrating promising results with a simplified clinical workflow based on CT alone. Our code is publicly available via <monospace xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><uri>https://github.com/yousefis/DenseUnet_Esophagus_Segmentation</uri></monospace> .

Breast mass segmentation in ultrasound with selective kernel U-Net convolutional neural network

In this work, we propose a deep learning method for breast mass segmentation in ultrasound (US). Variations in breast mass size and image characteristics make the automatic segmentation difficult. To address this issue, we developed a selective kernel (SK) U-Net convolutional neural network. The aim of the SKs was to adjust network's receptive fields via an attention mechanism, and fuse feature maps extracted with dilated and conventional convolutions. The proposed method was developed and evaluated using US images collected from 882 breast masses. Moreover, we used three datasets of US images collected at different medical centers for testing (893 US images). On our test set of 150 US images, the SK-U-Net achieved mean Dice score of 0.826, and outperformed regular U-Net, Dice score of 0.778. When evaluated on three separate datasets, the proposed method yielded mean Dice scores ranging from 0.646 to 0.780. Additional fine-tuning of our better-performing model with data collected at different centers improved mean Dice scores by ∼6%. SK-U-Net utilized both dilated and regular convolutions to process US images. We found strong correlation, Spearman's rank coefficient of 0.7, between the utilization of dilated convolutions and breast mass size in the case of network's expansion path. Our study shows the usefulness of deep learning methods for breast mass segmentation. SK-U-Net implementation and pre-trained weights can be found at github.com/mbyr/bus_seg.

Dense Dilated Convolutions’ Merging Network for Land Cover Classification

Land cover classification of remote sensing images is a challenging task due to limited amounts of annotated data, highly imbalanced classes, frequent incorrect pixel-level annotations, and an inherent complexity in the semantic segmentation task. In this article, we propose a novel architecture called the dense dilated convolutions' merging network (DDCM-Net) to address this task. The proposed DDCM-Net consists of dense dilated image convolutions merged with varying dilation rates. This effectively utilizes rich combinations of dilated convolutions that enlarge the network's receptive fields with fewer parameters and features compared with the state-of-the-art approaches in the remote sensing domain. Importantly, DDCM-Net obtains fused local- and global-context information, in effect incorporating surrounding discriminative capability for multiscale and complex-shaped objects with similar color and textures in very high-resolution aerial imagery. We demonstrate the effectiveness, robustness, and flexibility of the proposed DDCM-Net on the publicly available ISPRS Potsdam and Vaihingen data sets, as well as the DeepGlobe land cover data set. Our single model, trained on three-band Potsdam and Vaihingen data sets, achieves better accuracy in terms of both mean intersection over union (mIoU) and F1-score compared with other published models trained with more than three-band data. We further validate our model on the DeepGlobe data set, achieving state-of-the-art result 56.2% mIoU with much fewer parameters and at a lower computational cost compared with related recent work. Code available at https://github.com/samleoqh/DDCM-Semantic-Segmentation-PyTorch

Fuzzy cerebellar model articulation controller network optimization via self-adaptive global best harmony search algorithm

Fuzzy cerebellar model articulation controller (FCMAC) networks with excellent nonlinear appropriation ability and simple implementation are used to solve complex uncertainties problems in engineering applications. Both online and off-line learning algorithm of FCMAC networks usually applies the gradient-descent-type methods. However, such gradient-descent methods lead to the high possibility to converging into local minima. To cope with the local minimum problem, this paper alternatively proposes to apply harmony search algorithm to find optimal network parameters, so as to achieve better performances of FCMAC. The harmony search algorithm optimizes not only FCMAC network’s weight variables, but also optimizes network receptive field’s center position and standard deviation parameters. In order to obtain an optimal network, the weight values, center positions, and standard deviations are transformed to three data strings that can be processed by harmony search algorithm. In particular, the self-adaptive global best harmony search algorithm (SGHS) is used to search optimal parameter combinations of FCMAC within solution domains. The network’s performances are verified by approximating six nonlinear formulae. In order to compare the performances of the FCMAC networks optimized by the SGHS algorithm, a back-propagation trained network and another harmony search variant optimized networks are also tested in this work. The experimental results show that the networks optimized by SGHS perform the faster convergence speed and better accuracy.

Network Receptive Field Modeling Reveals Extensive Integration and Multi-feature Selectivity in Auditory Cortical Neurons.

Cortical sensory neurons are commonly characterized using the receptive field, the linear dependence of their response on the stimulus. In primary auditory cortex neurons can be characterized by their spectrotemporal receptive fields, the spectral and temporal features of a sound that linearly drive a neuron. However, receptive fields do not capture the fact that the response of a cortical neuron results from the complex nonlinear network in which it is embedded. By fitting a nonlinear feedforward network model (a network receptive field) to cortical responses to natural sounds, we reveal that primary auditory cortical neurons are sensitive over a substantially larger spectrotemporal domain than is seen in their standard spectrotemporal receptive fields. Furthermore, the network receptive field, a parsimonious network consisting of 1–7 sub-receptive fields that interact nonlinearly, consistently better predicts neural responses to auditory stimuli than the standard receptive fields. The network receptive field reveals separate excitatory and inhibitory sub-fields with different nonlinear properties, and interaction of the sub-fields gives rise to important operations such as gain control and conjunctive feature detection. The conjunctive effects, where neurons respond only if several specific features are present together, enable increased selectivity for particular complex spectrotemporal structures, and may constitute an important stage in sound recognition. In conclusion, we demonstrate that fitting auditory cortical neural responses with feedforward network models expands on simple linear receptive field models in a manner that yields substantially improved predictive power and reveals key nonlinear aspects of cortical processing, while remaining easy to interpret in a physiological context.

Normative Visual Development: efficient coding principles for adult V1 predict properties of LGN waves prior to eye opening

We present a novel approach to understanding spontaneous activity in the LGN and V1 prior to natural visual experience. Patterned, spontaneous neural activity has been measured in these areas but is poorly understood in comparison to work on retinal waves [1]. Our predictions about LGN/V1 spontaneous activity not only have implications for future experiments, but provide an additional computational-level interpretation. In the same way that V1 can be understood through neural network receptive field models (Marr's algorithmic level) as well as an efficient coding of natural images (Marr's computational level), we propose that early visual spontaneous activity can be understood not only through neural network models of receptive field and map formation, as in many previous approaches [2,3], but also by how this activity relates to the high-level coding objectives of V1. The key insight in this work is that the form of spontaneous activity in the early visual system can be constrained by these normative principles to resemble measured spontaneous activity patterns. The neural code in fully-developed adult primary visual cortex (V1) is presumed to be an efficient code; by encoding images of our natural visual environment, techniques such as sparse coding [4] and independent components analysis [5] have produced linear filters which resemble experimentally measured receptive fields in V1. Our simulations show how patterns which qualitatively resemble such activity are capable of producing these V1-like visual codes by using the same learning algorithms. The spontaneous activity model is similar to a previous abstracted version of retinal wave generation [6] with the addition of multiple eye-layers and correlated interaction between the layers as has been measured experimentally [7]. All model parameters have a direct physiological interpretation and also relate to theoretical models used in the physics of critical phenomena (e.g. percolation networks). This normative approach demonstrates that binocular disparity-selective cells can be refined by spontaneous activity in a way that promotes early stereopsis. This unique, normative approach to visual development provides a way of applying the tools of efficient coding used in the adult visual system to better understand how the how V1 refines prior to visual experience.