WO2021165053A1 - Out-of-distribution detection of input instances to a model - Google Patents

Out-of-distribution detection of input instances to a model Download PDF

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Publication number
WO2021165053A1
WO2021165053A1 PCT/EP2021/052750 EP2021052750W WO2021165053A1 WO 2021165053 A1 WO2021165053 A1 WO 2021165053A1 EP 2021052750 W EP2021052750 W EP 2021052750W WO 2021165053 A1 WO2021165053 A1 WO 2021165053A1
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ood
model
input
main model
score
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French (fr)
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Nicola PEZZOTTI
Dimitrios Mavroeidis
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Koninklijke Philips NV
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Koninklijke Philips NV
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Priority to EP21702515.4A priority Critical patent/EP4107662A1/en
Priority to JP2022548651A priority patent/JP7768136B2/ja
Priority to CN202180015890.1A priority patent/CN115136192A/zh
Priority to US17/800,598 priority patent/US20230377314A1/en
Publication of WO2021165053A1 publication Critical patent/WO2021165053A1/en
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Definitions

  • the invention relates to a system for out-of-distribution detection of input instances to a model, and to a corresponding computer-implemented method.
  • the invention further relates to a system for enabling out-of-distribution detection, and to a corresponding computer-implemented method.
  • the invention also relates to a computer-readable medium.
  • the processing pipeline of data coming from medical imaging devices involves various complex image processing operations.
  • raw data coming from a scanner may be converted into an image to be inspected by a clinician, a task known as image reconstruction.
  • image reconstruction As another example, particular objects may be recognized and highlighted in an image produced by the medical imaging device, a task known as semantic segmentation.
  • Image analysis can also be used, for example, to locate pathologies.
  • image processing models generate an output image from an input instance, e.g., an input image, or raw scanner data represented in a so- called k-space representation (for MR scanners) or in a sinogram (for CT scanners).
  • Various embodiments relate to estimating whether an input instance to be processed by a model producing an output image, e.g., a deep neural network, was included in the dataset used for training, and accordingly, whether the model may be expected to produce reliable results.
  • a model producing an output image e.g., a deep neural network
  • a system for out-of-distribution (OOD) detection of input instances to a main model is proposed.
  • OOD out-of-distribution
  • a computer-implemented method of OOD detection of input instances to a main model is proposed.
  • the main model may be configured to generate an output image from an input instance.
  • the main model may be a machine-leamable model that has been, or is being, trained on a training dataset.
  • multiple secondary models may be used.
  • a secondary model may be trained on the same training dataset on which the main model is trained.
  • the secondary models Given an input instance, the secondary models may be applied to it to obtain respective secondary model output images.
  • a pixel OOD score may be determined as a variability among respective values of the pixel in the respective secondary model output images.
  • the pixel OOD scores may be combined into an overall OOD score indicating whether the input instance is OOD with respect to the training dataset. Based on the overall OOD score, an output signal may be generated indicating whether the input instance is OOD.
  • various aspects use multiple secondary models, trained on the same training dataset as the main model.
  • the multiple secondary models may together be referred to as an “ensemble” of secondary models.
  • a training dataset typically comprises multiple training input instances and corresponding training output images.
  • the main model may be trained to, given a training input instance, produce the corresponding training output image.
  • the secondary models may be trained on the same training dataset, in the sense that they may be trained to produce the same training output images given the same training input instances, or at least to produce outputs from inputs where these outputs and inputs are related to the original training outputs and inputs, e.g., by downscaling, channel reduction, or another image processing operation.
  • the secondary models may use the same model architecture as the main model (optionally, the main model can be one of the secondary models), or a variant of it, e.g., a simplification that has fewer trainable parameters.
  • respective secondary models may be trained by training the same trainable model based on respective random initializations of its set of parameters.
  • the secondary models may be expected to exhibit largely the same behaviour as the main model and as each other, when they are applied to input instances that are similar to the training data. Accordingly, at least when an input instance is input to the secondary models that is similar to the training data, or in other words, is in distribution (ID), the secondary models may generally produce similar results. Thus, the per-pixel variance of the output images of the secondary models may generally be low. However, when an input instance is out-of-distribution (OOD), the secondary models have not been trained to provide similar outputs for that input instance, and since they are separately trained, may generally have a higher per-pixel variance of their output images.
  • OOD out-of-distribution
  • each separate pixel OOD score of a pixel of the output image may be considered to be a measurement of whether the input instance is OOD or not, and accordingly, an overall assessment of the input instance being OOD may be obtained by combining pixel OOD scores of one or more pixels into an overall OOD score.
  • OOD detection may be performed for image generating models in an efficient and accurate way.
  • a relatively limited number of secondary models may suffice to obtain an accurate overall OOD score, for example, at most twenty or even at most ten or at most five.
  • the inventors have been able to get good results already with five secondary models.
  • each pixel OOD score may by itself be regarded as a measurement of the input instance being OOD or not, also with a limited number of secondary models, sufficient data may be available to determine OOD-ness of the input instance.
  • secondary models with fewer trainable parameters and/or smaller inputs and/or smaller outputs the overhead of computing the OOD score with respect to applying the main model may be limited.
  • Another advantage of the provided OOD detection techniques is that they are largely model-agnostic, e.g., not relying on a particular model architecture of the main model and/or secondary models.
  • a system for enabling out-of-distribution (OOD) detection of inputs to a main model is proposed.
  • OOD out-of-distribution
  • a corresponding computer-implemented method is proposed.
  • multiple secondary models may be trained on the same training dataset on which the main model has been trained. The secondary models may then be associated with the main model to enable the OOD detection.
  • a computer-readable medium is proposed comprising transitory or non-transitory data representing one or more of instructions for performing a computer-implemented method as described herein, or secondary models associated with main model to enable OOD detection as described herein.
  • the OOD detection techniques described herein may be applied for medical image processing.
  • Various models for medical image processing are known in the art per se and may be combined with the presented techniques.
  • the output image of the main model may be determined from input data of a medical imaging device, for example, a CT scanner or an MR scanner.
  • a medical imaging device for example, a CT scanner or an MR scanner.
  • being able to do OOD detection as described herein may enable to safely use undersampled k-space data (e.g., obtained by accelerated scanning) since the output image may be flagged as OOD if the input instance is not sufficiently similar to known training examples to apply the main model. Since less data has to be acquired in the scanner, examination time can be reduced while still getting reliable results.
  • the use of OOD detection techniques may enable to safely apply a lower dose with reliable results, resulting in lower radiation for patients.
  • this input data can be a signal produced by the medical imaging device.
  • the signal may be represented in k-space or in image space by applying the inverse Fourier transform to the k-space representation.
  • the signal may be represented as a sinogram or in image space by applying the inverse Radon transform to the sinogram representation.
  • the main model can for example be a medical image reconstruction model configured to reconstruct the input image from the signal. Such a reconstruction model may also be referred to, or comprise, a denoising model.
  • a CT image may be reconstructed from a CT signal or a MR image may be reconstructed from a MR signal, although the model can also be trained, for example, to reconstruct a CT image from a MR signal or a MR image from a CT signal.
  • a medical image processor model can also operate on an input image reconstructed from such a signal.
  • the main model can be a segmentation model, e.g., a semantic segmentation model, for use in medical image processing or in other application domains.
  • a segmentation model may be configured to indicate a part of an input instance representing a particular characteristic, e.g., an object or other type of aspect that can be located in an image.
  • a characteristic can be any particular type of object that can be present at a particular location in the input instance (e.g., a cyst, a tumour, a cell nucleus, a lymphocyte, a necrotic tissue, etc.), or a particular characteristic that an object present in the input instance may have (e.g., dark, noisy, spiky, etc.).
  • the main model may provide, per image pixel, an indication of whether the pixel belongs to the characteristic.
  • the main model may also be configured to indicate, for respective pixels of the input instance, respective amounts, or extents, of presence of the characteristic (e.g., a cell or nuclei density, a perfusion in tissue, etc.) at that pixel location.
  • the main model can also be a medical image analysis model configured to determine an output image that locates a pathology in an input image; such a model may operate on a reconstructed image or on the signal of the medical imaging device, as desired.
  • the main model may be a tumour detection model, e.g., for prostate or ovarian tumour, or a tumour grading model configured to assign abnormality values to parts of a tumour identified in the input image.
  • an output signal may be generated based on the overall OOD score, indicating whether the input instance is OOD.
  • Such an output signal can be used in various ways, e.g., by a user or in further automated processing.
  • the overall OOD score maybe used to decide whether to apply the main model to the input instance.
  • the main model may be applied to the input instance to obtain a main model output image, and the main model output image may be output, e.g., to a user in a sensory perceptible manner, or digitally for further automated processing.
  • the main model may be applied to the input instance also for input instances that are indicated to be OOD, e.g., in such cases, the output image may be shown along with a warning or error that the input instance is determined to be OOD.
  • the output signal may further indicate one or more pixels of the output images contributing to the input instance being OOD, for example, a subset of pixels with the highest pixel OOD scores.
  • the indicated pixels can be pixels whose OOD scores exceed a threshold, or they can be a fixed percentage or number of pixels with the highest OOD scores.
  • a possible cause for an input instance being OOD can be an input instance that is of too low quality.
  • the input instance may represent a “routine case” for which the main model can still confidently provide a model output.
  • the secondary models may also consistently provide similar output images. If the input instance is less similar to the training dataset, however, the secondary models may diverge, and thus there is less confidence in the main model output. Accordingly, the input instance may be determined to be OOD.
  • the input instance may be data from a CT scanner operating at a too low dose to reliably produce an output image for a particular subject being scanned, or an MR scanner operating at a too high acceleration.
  • a new measurement of the input instance e.g., a new CT or MR scan
  • a higher quality e.g., higher dose or lower acceleration
  • this input instance may be used further, e.g., presented to a user or processed automatically.
  • this process may be repeated for multiple quality settings.
  • an input instance being OOD may be a measurement artefact in the input instance.
  • a measurement artefact due to a movement of the subject being scanned in a medical imaging device, or a metal artefact, or the like. Accordingly, instead of or in addition to performing a new measurement at a higher quality, also a new measurement at the same quality may be performed. If the new input instance is not OOD, it may be used further, the previous input instance being disregarded as an artefact.
  • Another possible cause for an input instance being OOD is that the subject being measured by the input instance is out-of-distribution.
  • the subject being scanned may have a pathology that is underrepresented in the dataset. This cause may be recognized by determining that multiple input instances representing the same subjects are OOD, but input instances of other subjects are not OOD.
  • the subject may be reported to a user, e.g., a clinician, for further analysis.
  • another output image for the input instance may be determined using a fallback model and the other output image may be used instead of the output image of the main model.
  • the fallback model can for instance be a non-trainable model. For example, for MR scans, a SENSE-based reconstruction as known per se may be used as a fallback if the subject is OOD.
  • Another possible cause for input instance being OOD can be a persistent measurement problem, e.g., a defect in the measurement device or wrong environment conditions for the measurement. This cause may be recognized by determining that input instances representing multiple subjects are OOD. In such a case, the persistent measurement problem may be reported for fixing.
  • a persistent measurement problem e.g., a defect in the measurement device or wrong environment conditions for the measurement. This cause may be recognized by determining that input instances representing multiple subjects are OOD. In such a case, the persistent measurement problem may be reported for fixing.
  • Fig. 1 shows a system for enabling out-of-distribution (OOD) detection of inputs to a main model
  • Fig. 2 shows a system for out-of-distribution (OOD) detection of input instances to a main model
  • Fig. 3 shows a detailed example of a model for use with the techniques described herein, in this case, a U-Net type model
  • Fig. 4 shows a detailed example of how to determine an overall OOD score for an input instance
  • Fig. 5 shows a computer-implemented method of out-of-distribution (OOD) detection of input instances to a main model
  • Fig. 6 shows a computer-implemented method of enabling out-of-distribution (OOD) detection of inputs to a main model
  • Fig. 7 shows a computer-readable medium comprising data.
  • Fig. 1 shows a system 100 for enabling out-of-distribution (OOD) detection of inputs to a main model.
  • the main model may be configured to generate an output image from an input instance.
  • the main model may have been trained on a training dataset.
  • the system 100 may comprise a data interface 120 and a processor subsystem 140 which may internally communicate via data communication 121.
  • Data interface 120 may be for accessing data 030 representing the training dataset on which the main model is trained.
  • Data interface 120 can also be for accessing the main model and/or multiple secondary models 040, as discussed in more detail below.
  • the secondary models 040 may be used for OOD detection according to a method described herein, e.g., by system 200 of Fig. 2.
  • the enabling of OOD detection and the OOD detection itself may be combined in a single system or method, e.g., systems 100 and 200 may be combined into a single system.
  • the system e.g., its processor subsystem, may be further configured to train the main model on training dataset 030.
  • the processor subsystem 140 may be configured to, during operation of the system 100 and using the data interface 120, access data 030, 040.
  • the data interface 120 may provide access 122 to an external data storage 021 which may comprise said data 030, 040.
  • the data 030, 040 may be accessed from an internal data storage which is part of the system 100.
  • the data 030, 041 may be received via a network from another entity.
  • the data interface 120 may take various forms, such as a network interface to a local or wide area network, e.g., the Internet, a storage interface to an internal or external data storage, etc.
  • the data storage 021 may take any known and suitable form.
  • Processor subsystem 140 may be configured to, during operation of the system 100 and using the data interface 120, train multiple secondary models 040.
  • a secondary model 040 may be trained on the training dataset 030 on which the main model is trained.
  • a secondary model 040 may be for determining a secondary model output image for an input instance for use in the OOD detection.
  • Processor subsystem 140 may be further configured to associate the multiple secondary models 040 with the main model to enable the OOD detection.
  • the secondary models may be associated with the main model, or more specifically with data representing the main model, in any suitable manner, e.g., by including the secondary models in the model data itself, e.g., as a file header, XML element, etc., or providing the secondary models as a separate file, or in any other manner.
  • the secondary models 040 may be stored in a same data container as the main model, for example in a same file(s), but may also be provided as separate secondary models associated with the main model.
  • the main model may link to the secondary models, e.g., by containing an URL at which the secondary models 040 are accessible, or the secondary models 040 may link to the main model.
  • the secondary models 040 may link to the main model.
  • Various other means of association are equally conceivable and within reach of the skilled person.
  • the system 100 may comprise an input interface (not shown) for obtaining sensor data from a sensor, for example, a signal produced by a medical imaging device such as a CT scanner or an MR scanner.
  • a medical imaging device such as a CT scanner or an MR scanner.
  • One or more training input instances of the training dataset may be based on such sensor data.
  • Obtaining of input instances via an input interface is discussed in more detail with respect to Fig. 2 and the options described there can be applied in system 100 as well.
  • the sensor itself which is configured to measure the sensor data e.g., the CT scanner or the MR scanner, may be part of the system 100.
  • the system 100 may be embodied as, or in, a single device or apparatus, such as a workstation, e.g., laptop or desktop-based, or a server.
  • the device or apparatus may comprise one or more microprocessors which execute appropriate software.
  • the processor subsystem may be embodied by a single Central Processing Unit (CPU), but also by a combination or system of such CPUs and/or other types of processing units.
  • the software may have been downloaded and/or stored in a corresponding memory, e.g., a volatile memory such as RAM or a non-volatile memory such as Flash.
  • the functional units of the system may be implemented in the device or apparatus in the form of programmable logic, e.g., as a Field-Programmable Gate Array (FPGA) and/or a Graphics Processing Unit (GPU).
  • FPGA Field-Programmable Gate Array
  • GPU Graphics Processing Unit
  • each functional unit of the system may be implemented in the form of a circuit.
  • the system 100 may also be implemented in a distributed manner, e.g., involving different devices or apparatuses, such as distributed servers, e.g., in the form of cloud computing.
  • Fig. 2 shows a system 200 for out-of-distribution (OOD) detection of input instances to a main model.
  • OOD out-of-distribution
  • the main model may be configured to generate an output image from an input instance.
  • the main model may have been trained on a training dataset.
  • the system 200 may comprise a data interface 220 and a processor subsystem 240 which may internally communicate via data communication 221.
  • Data interface 220 may be for accessing data 040 representing multiple secondary models for use in the OOD detection.
  • a secondary model may be trained on the same training dataset on which the main model is trained.
  • Data interface 220 can also be for accessing the main model.
  • the secondary model data may be obtained from a system for enabling OOD detection, e.g., system 100 of Fig., 1, or by performing a method for enabling OOD detection as described herein.
  • the processor subsystem 240 may be configured to, during operation of the system 200 and using the data interface 220, access data 040.
  • the data interface 220 may provide access 222 to an external data storage 022 which may comprise said data 040.
  • the data 040 may be accessed from an internal data storage which is part of the system 200.
  • the data 040 may be received via a network from another entity.
  • the data interface 220 may take various forms, such as a network interface to a local or wide area network, e.g., the Internet, a storage interface to an internal or external data storage, etc.
  • the data storage 022 may take any known and suitable form.
  • Processor subsystem 240 may be configured to, during operation of the system 200 and using the data interface 220, obtain an input instance. Processor subsystem 240 may be further configured to apply the respective multiple secondary models to obtain respective secondary model output images. Processor subsystem 240 may be further configured to determine pixel OOD scores of pixels of the respective secondary model output images. A pixel OOD score of a pixel may be determined as a variability among respective values of the pixel in the respective secondary model output images. Processor subsystem 240 may further combine the determined pixel OOD scores into an overall OOD score. The overall OOD score may indicate whether the input instance is OOD with respect to the training dataset.
  • Processor subsystem 240 may further generate an output signal 225 based on the overall OOD score, the output signal 225 being indicative of whether the input instance is OOD.
  • the output signal can be the overall OOD score itself, or an alert raised if input instance is OOD.
  • the output signal may further indicate one or more pixels of the output images contributing to the input instance being OOD, thus providing an explanation of why the input instance is OOD, that can be output to a rendering device or to another software component for further automated processing.
  • processor subsystem 240 may apply the main model to the input instance to obtain a main model output image, and output the main model output image, for example, to a user via an output interface as discussed below, or to another software component for further automatic processing.
  • the OOD score may be compared against a threshold OOD score, e.g., a fixed score or a score associated with the secondary models.
  • OOD scores for multiple input instances of a dataset can be determined to compute a similarity between the dataset and the training dataset, without necessarily applying the main model to these input instances.
  • the system 200 may comprise an input interface 260 for obtaining sensor data 223 from a sensor, for example, from a signal 224 produced by a medical imaging device such as a CT scanner or an MR scanner. Shown in the figure is an MR scanner 072.
  • the signal can be a raw signal from the medical imaging device, e.g., represented in k-space (in the case of an MR scanner) or as a sinogram (in the case of a CT scanner), or transformed into image space, e.g. by an inverse Fourier Transform or an inverse Radon transform, respectively.
  • the MR scanner may be configured to perform an accelerated scan, for example, with an acceleration factor of at least two, at least four, or at least six.
  • successful reconstruction or analysis of the MR data may still be possible using an appropriate trained model, but there is a higher risk of wrong results for inputs that are underrepresented in the training dataset, making OOD detection particularly important.
  • Similar considerations apply in the case of CT scanners operating at a low dose, for example, at most half of the full dose or at most a quarter of the full dose.
  • the sensor can be a camera producing images, a video camera producing a video, etc.
  • input interface 260 may be configured for various types of sensor signals, e.g., video signals, radar/LiDAR signals, ultrasonic signals, etc.
  • the input instance on which OOD detection is performed may be based on sensor data 223, for example, the input instance be equal to sensor data 223 or an optional pre-processing step may be performed on it.
  • the sensor itself which is configured to measure the signal 224 e.g., the CT scanner or the MR scanner 072, may be part of the system 200.
  • the system 200 may comprise a display output interface 280 or any other type of output interface for outputting the output signal 225 to a rendering device, such as a display 290.
  • the display output interface 280 may generate display data 282 for the display 290 which causes the display 290 to render the output signal in a sensory perceptible manner, e.g., as an on-screen visualisation 292.
  • an error or warning message may be shown if the input instance is OOD, for example, alongside the model output of the main model.
  • particular pixels of the secondary model output images contributing to the input instance being OOD may also be rendered, e.g., highlighted on the output image of the main model.
  • the system 200 may be embodied as, or in, a single device or apparatus, such as a workstation, e.g., laptop or desktop-based, or a server.
  • the device or apparatus may comprise one or more microprocessors which execute appropriate software.
  • the processor subsystem may be embodied by a single Central Processing Unit (CPU), but also by a combination or system of such CPUs and/or other types of processing units.
  • the software may have been downloaded and/or stored in a corresponding memory, e.g., a volatile memory such as RAM or a non-volatile memory such as Flash.
  • the functional units of the system may be implemented in the device or apparatus in the form of programmable logic, e.g., as a Field-Programmable Gate Array (FPGA) and/or a Graphics Processing Unit (GPU).
  • FPGA Field-Programmable Gate Array
  • GPU Graphics Processing Unit
  • each functional unit of the system may be implemented in the form of a circuit.
  • the system 200 may also be implemented in a distributed manner, e.g., involving different devices or apparatuses, such as distributed servers, e.g., in the form of cloud computing.
  • Fig. 3 shows a detailed, yet non-limiting, example of a model for use with the techniques described herein.
  • a main model and/or one or more of the secondary models for use in the techniques described herein may be built according to the model architecture described in this figure.
  • the particular example shown in this figure is a fully convolutional neural network, more specifically, a U-Net-type model.
  • Such a model may be used, e.g., for various image-to-image translations, including reconstruction of images from a medical imaging device.
  • the model shown here determines an output image OIM, 350, for an input instance IIN, 330.
  • the number of channels does not need to correspond to different colours however and in that sense the input instance IIN may also be more generally referred to as an input volume.
  • the output image OIM in this example is an image of the same spatial dimensions as the input instance IIN, e.g., with the same width and height.
  • the output image OIM can have the same number of channels as the input image but the number of channels can also be different.
  • the model here is an example of a convolutional network, also called a convolutional neural network.
  • the term convolutional network may be used to refer to any neural network that comprises at least one convolutional layer.
  • a convolutional layer is a layer which operates by performing a convolution, or sliding dot product, operation. Accordingly, in a convolutional layer, a m x n x c-sized input volume may be transformed into am' x n' x c'-sized output volume using c' filters that each convolve over the input volume.
  • the number of filters at a layer can be at most or at least 8, at most or at least 32, or at most or at least 128.
  • the spatial dimensions m' x n' of the output of a layer can be different from the spatial dimensions m x n of its input, although generally a spatial correspondence with the input IIN is maintained.
  • the spatial dimensions of the output of a layer can be smaller than its input, e.g., the convolutional layer may perform a downsampling.
  • the spatial dimensions of the output of the layer can also be larger than the spatial dimensions of the input, e.g., the layer may be a so-called “up- convolution” layer implemented by upsampling of the input feature map and then applying a convolution operation.
  • Convolutional neural networks can comprise various other types of layers in addition to convolutional layers, e.g., one or more ReLU layer and/or one or more pooling layers.
  • the number of convolutional layers in a convolutional network can for example be at least 5, or at least 10
  • the model shown in this figure is a so-called fully convolutional network.
  • Such a model transforms input instance IIN into an output image OIM in a sequence of layers that each preserve a spatial correspondence with the input instance, e.g., convolutional layers, pooling layers, ReLU layers, etc.
  • the model in this figure is an encoder-decoder model.
  • a contracting part CP 310 (also known as an “encoder path”) and an expansive part EP, 320 (also known as a “decoder path”).
  • the contracting part CP may comprise one or more layers that produce subsequent activation volumes for input instance IIN. Shown in the figure are activation volumes AVI, 341, AV2, 342, up to AVk-1, 343 and AVk, 344.
  • An activation volume may be determined from a previous activation volume by one or more layers of the model, as illustrated by arrows 361, 362, up to 363 and 364: typically, a max-pooling followed by one or more convolutional layers with associated ReLU operations.
  • the spatial dimensions of the activation volumes are typically decreased in size throughout the contracting part CP, e.g., activation volume AV2 may have smaller spatial dimensions than activation volume AVI (although the number of channels may actually increase), and similarly for the other activation volumes shown.
  • the activation volume AVk resulting from the contracting part CP of the U-net model may then be processed in the expansive part EP.
  • the expansive part may comprise one or more layers that produce subsequent activation volumes, e.g., activation volumes AVk+1, 345, up to AV2k-2, 346 and finally output image OIM.
  • an activation volume may be determined from a previous activation volume by one or more layers of the model, as illustrated by arrows 365 up to 366 and 367.
  • an up-convolution e.g., an upsampling followed by a convolution
  • one or more convolutional layers with associated ReLU operations may be used, followed by one or more convolutional layers with associated ReLU operations.
  • the spatial dimensions of the activation volumes are typically increased in size, e.g., activation volume AVk+1 may have larger spatial dimensions than activation volume AVk (although the number of channels may decrease), and similarly for the other activation volumes shown.
  • the expansive part EP can optionally comprise so-called skip connections, in which an activation volume AVi of the contracting part CP may be concatenated with an activation volume of the expansive part EP.
  • An encoder-decoder model with one or more skip connections may be referred to as a U-Net type model.
  • the result of an up-convolution may be concatenated with a corresponding activation volume of the contracting part CP after which one or more convolutions may be applied.
  • the feature map of the contracting part may be cropped to account for border pixels.
  • activation volume AVk-1 may be concatenated with the upconvolution of activation volume AVk, from the result of which activation volume AVk+1 may then be determined.
  • the determination of activation volume AV2k-2 may use a skip connection 366’ to a respective activation volume AV2; the determination of activation volume OIM may use a skip connection 367’ to respective activation volume AVI, etc.
  • U-Net Convolutional Networks for Biomedical Image Segmentation
  • ResNet Residual Network
  • Fig. 4 shows a detailed, yet non-limiting, example of how to determine an overall out-of- distribution (OOD) score for an input instance to a main model, and thereby perform OOD detection of the input instance.
  • OOD out-of- distribution
  • OOD detection may be performed in the form of the determination of an overall OOD score OODS, 485.
  • an input IIN may be given to several secondary models SMi, 441-442.
  • the outputs SOi, 451-452, may then be used to create a so called OOD image OODI, 475.
  • the value of a pixel of the OOD image OODI may represent a variability of the corresponding pixels in the output images SOi of the models SMi.
  • An OOD value OODS may then be obtained by reducing the OOD image OODI, e.g., by averaging the OOD image, taking the maximum, or the minimum.
  • the OOD score OODS may be used to assess if the input IIN to the model MM is in or outside the training distribution. Such an assessment may be a good indicator of the resulting quality of the models in the ensemble and/or the main model MM.
  • the input may also be processed by the main model MM, 440, which may produce the main output image OI, 450 (e.g., a reconstructed MR image, a denoised CT image, etc.), denoised image in CT).
  • the main model MM can be bigger than the secondary models SMi, e.g., in terms of number of parameters, thus allowing for a higher quality main output OI, while keeping the compute time of the OOD score computation OODS under control.
  • the input instance IIN can be an input image, e.g., comprising one, three, or another number of channels.
  • the image may be captured by a camera, but it is also possible to use other type of sensor data, e.g., audio data or time-series data of multiple sensor measurements, represented as an image. It is also not necessary for input instance IIN to be an image.
  • input instance IIN may be a feature vector from which the main model generates an output image, e.g., a latent representation of a generator part of a Generative Adversarial Network (GAN) or a decoder part of an autoencoder, e.g., a Variational Autoencoder (VAE).
  • GAN Generative Adversarial Network
  • VAE Variational Autoencoder
  • input instance IIN can represent synthetic data from which a synthetic output image is to be generated, but input instance IIN can also represent a real-world input, e.g., by being determined as or based on the output of the encoder part of the autoencoder.
  • the input instance IIN can represent a signal produced by a medical imaging device, e.g., for use in a medical image reconstruction or medical image analysis task.
  • a medical imaging device e.g., for use in a medical image reconstruction or medical image analysis task.
  • the input instance may represent the scanner signal in so-called k-space, or in the image space resulting from applying an inverse Fourier transform to the k-space data.
  • the input instance may represent the scanner signal as a sinogram, or in image space by applying the inverse Radon transform.
  • the input instance IIN can comprise extra information in addition to the sensor/image data, e.g., metadata such as log data or patient-specific information that can help determine a more accurate output.
  • the main model may be an image processing model.
  • image processing model is used here to refer to a model that has an image, e.g., a volume with a width, a depth, and a number of channels (which can be one, three, or any other number), as output (but does not need to have an image as input).
  • OI the output image of the main model MM is shown in the figure as OI, 450.
  • the output image OIM can have a single channel, as may be the case for various segmentation models, MR or CT reconstruction models, etcetera; three channels, as may be the case for various generative models, image-to-image translation models, etcetera; or any other number of channels as appropriate for the application at hand.
  • the output image can be discrete, e.g., binary, e.g., in case of a mask; or continuous, e.g., in case of a generative model.
  • the output image in many cases has the same spatial dimensions as the input, possibly up to border effects.
  • the main model MM has been trained on a training dataset (not shown): typically, a labelled dataset comprising multiple training input instances and corresponding desired training output images (for example, at least 1000 or at least 1000000 training instances).
  • the main model is a trainable model (also known as a machine-leamable model or machine learning model).
  • Such a trainable model is typically trained by learning values for a set of trainable parameters.
  • the number of parameters of the main model may be at least 1000, at least 100000 or at least 10 million. It is beneficial from the point of view of efficiency of training to use a model which is amenable to gradient-based optimization, e.g., which is continuous and/or differentiable in its set of parameters.
  • the main model MM may be a U-net type model, or more generally, any type of encoder-decoder model, fully convolutional neural network, convolutional neural network, or other type of neural network, as discussed with respect to Fig. 3.
  • Such neural networks can also be used as part of a larger model, for example, in one or more iterations of an iterative model as done, for example, in “Adaptive-CS-Net: FastMRI with Adaptive Intelligence” by N. Pezzotti et al.
  • the main model can be a generative model, e.g., the generative part of a GAN or the decoder part of a VAE.
  • neural networks are also known as artificial neural networks.
  • the set of parameters may comprise weights of nodes of the neural network.
  • the number of layers of the model may be at least 5 or at least 10, and the number of nodes and/or weights may be at least 1000 or at least 10000.
  • various known architectures for neural networks and other types of machine leamable models may be used.
  • multiple secondary models SMi may be used. Shown in the figure are secondary models SMI, 441, up to SMm, 442. For example, at most or at least five or at most or at least ten secondary models may be used.
  • respective secondary model output images SMi may be obtained, as illustrated in the figure by secondary model output images SOI, 451, up to SOm, 452.
  • secondary models SMi may be models that are trained on the same training dataset as the main model MM. Accordingly, the secondary models SMi may be expected to exhibit similar behaviour as the main model, and as each other, when applied to input instances IIN that come from the training dataset or are similar to instances from the training dataset. Accordingly, a relatively low per-pixel variability among outputs of the secondary models may be expected. However, on input instances IIN that do not come from the training dataset, there are no such guarantees, and accordingly, a higher per-pixel variability may be expected.
  • the secondary models SMi may be trained on downscaled training input instances.
  • such a secondary model may be applied to an input instance IIN by first downscaling the input instance.
  • One, several, or all of the secondary models may, instead or in addition, be trained on downscaled training output images, and accordingly, in use, produce smaller output images that can later be upscaled if necessary.
  • the inputs and/or outputs may be downscaled by at least a factor two, or at least a factor four.
  • the use of smaller inputs and/or outputs may enable to use smaller secondary models, e.g., having fewer trainable parameters than the main model, leading to reduced storage and computational requirements. It is also possible to simplify the secondary models to reduce the number of trainable parameters in other ways, e.g., by using a neural network with fewer layers, by using an iterative model with fewer iterations, etcetera. For example, a secondary model may have at most one half, at most 25%, or at most 10% of the number of trainable parameters as the main model.
  • a secondary model may also be an iterative model with at most half, at most 25%, or at most 10% of the number of iterations, instead of or in addition to reducing the number of parameters used in a single iteration.
  • the inventors have obtained good results for a main model with 15 iterations, by using secondary models with 3 iterations.
  • the secondary models SMi have a common model architecture, e.g., they may each be trained by initializing a set of parameters of the common model of and optimizing that set of parameters based on the initialization, but using different random initializations.
  • This common architecture can be the same as or different from the architecture of the main model MM. This technique has the advantage of being generally applicable and being well amenable to parallelization, both in training and in using the secondary models.
  • the main model MM is shown separately from the secondary models SMi in this figure, the main model can be used as one of the secondary models, e.g., both to determine a main model output and to determine a secondary model output.
  • the main model MM can also be composed of several or all of the secondary models, e.g., the main model output may be determined based on outputs of one or more of the secondary models SMi, e.g., by averaging or another type of combination operation.
  • the secondary model output images SOi may be used to determine pixel OOD scores of pixels of the respective secondary model output images SOi. For example, a pixel OOD score of the top-left pixel with coordinate (1,1) of the respective images SOi may be determined, and similarly for other pixels (t,y). In some embodiments, a pixel OOD score may be determined for each pixel. However, it is not needed to determine pixel OOD scores for all pixels and instead a sample of pixels can be taken instead, e.g., for efficiency reasons. The pixel OOD scores for several or all of the pixels may themselves be regarded to form an image that may be referred to as “OOD image” for the input instance IIN. Shown in the figure is OOD image OODI, 475.
  • operation PXS may comprise resizing (for example, downscaling the images to the smallest size) and/or channel reducing secondary model output images SOi to make their sizes correspond (for example, converting the images to greyscale).
  • a pixel OOD score of a pixel may be determined as a variability among respective values of the pixel in the respective secondary model output images.
  • the variability may be determined as a variability measure of a vector comprising pixel values for the secondary output images SOi, e.g., greyscale pixel values between 0 and 1, discretized pixel values, etcetera. Any appropriate variability measure can be taken, e.g., a variance or standard deviation; a Shannon entropy; etcetera.
  • the output image can be converted into a single-channel image, e.g., converting to greyscale.
  • the pixel OOD score may be obtained by combining the per-channel scores (e.g., as a maximum, minimum, or average), or by considering the vector of per- channel scores to be the pixel OOD score.
  • OODI of pixels of the secondary model output images SOi these scores may be combined, in a combining operation CMB, 480, into an overall OOD score OODS, 485.
  • the overall OOD score OODS may indicate whether the input instance is OOD with respect to the training dataset.
  • a maximum, minimum, or average may be used, or any other computation that generally provides a higher score for higher pixel OOD scores OODI, e.g., a function that is non-decreasing or increasing in each of the pixel OOD scores.
  • OODI e.g., a function that is non-decreasing or increasing in each of the pixel OOD scores.
  • Different score types provide different indications of OOD-ness that may be useful in different situations.
  • the maximum may be used as a high-assurance option to ensure that there is no part of the output image for which the secondary models diverge, and accordingly, to ensure that each part of the output image of the main model is trustworthy.
  • the average and minimum may be used to obtain a more global measure of trustworthiness of the main model output.
  • the different measures provide different kinds of information about OOD-ness of the input instance IIN
  • multiple OOD score values may be output, e.g., the overall OOD score may comprise respective constituent OOD score values, e.g., a maximum and an average.
  • a threshold OOD score may be applied.
  • the threshold score may be determined automatically based on OOD scores determined for multiple input instances to the main model.
  • the threshold score may be determined as a threshold of a statistical test of an overall OOD score belonging to the statistical distribution of OOD scores of in-distribution input instances.
  • the threshold score can be computed, e.g., as an optimal threshold score for a training set (containing in-distribution samples) and a hold out set (containing out-of-distribution samples).
  • the main model is trained by the same system as the secondary models, although it is also possible to obtain a pre-trained main model and train secondary models to enable OOD detection on it.
  • training is performed using stochastic approaches such as stochastic gradient descent, e.g., using the Adam optimizer as disclosed in Kingma and Ba, “Adam: A Method for Stochastic Optimization” (available at https://arxiv.org/abs/1412.6980 and incorporated herein by reference).
  • such optimization methods may be heuristic and/or arrive at a local optimum.
  • Training may be performed on an instance-by-instance basis or in batches, e.g., of at most or at least 64 or at most or at least 256 instances.
  • Fig. 5 shows a block-diagram of computer-implemented method 500 of out-of-distribution (OOD) detection of input instances to a main model.
  • the main model may be configured to generate an output image from an input instance.
  • the main model may be trained on a training dataset.
  • the method 500 may correspond to an operation of the system 200 of Fig. 2. However, this is not a limitation, in that the method 500 may also be performed using another system, apparatus or device.
  • the method 500 may comprise, in an operation titled “ACCESSING SECONDARY MODELS”, accessing 510 data representing multiple secondary models for use in the OOD detection.
  • a secondary model may be trained on the same training dataset on which the main model is trained.
  • the method 500 may comprise, in an operation titled “OBTAINING INPUT INSTANCE”, obtaining 520 an input instance.
  • the method 500 may comprise, in an operation titled “APPLYING SECONDARY MODELS”, applying 530 the respective multiple secondary models to obtain respective secondary model output images.
  • the method 500 may comprise, in an operation titled “DETERMINING OOD SCORES OF PIXELS”, determining 540 pixel OOD scores of pixels of the respective secondary model output images.
  • a pixel OOD score of a pixel may be determined as a variability among respective values of the pixel in the respective secondary model output images.
  • the method 500 may comprise, in an operation titled “COMBINING INTO OVERALL OOD SCORE”, combining 550 the determined pixel OOD scores into an overall OOD score.
  • the overall OOD score may indicate whether the input instance is OOD with respect to the training dataset.
  • the method 500 may comprise, in an operation titled “GENERATING OUTPUT SIGNAL”, generating 560 an output signal based on the overall OOD score, the output signal being indicative of whether the input instance is OOD.
  • Fig. 6 shows a block-diagram of computer-implemented method 600 of enabling out-of- distribution (OOD) detection of inputs to a main model.
  • the main model may be configured to generate an output image from an input instance.
  • the main model may be trained on a training dataset.
  • the method 600 may correspond to an operation of the system 100 of Fig. 1. However, this is not a limitation, in that the method 600 may also be performed using another system, apparatus or device.
  • the method 600 may comprise, in an operation titled “ACCESSING TRAINING DATASET”, accessing 610 data representing the training dataset on which the main model is trained.
  • the method 600 may comprise, in an operation titled “TRAINING SECONDARY MODELS”, training 620 multiple secondary models.
  • a secondary model may be trained on the training dataset on which the main model is trained.
  • a secondary model may be for determining a secondary model output image for an input instance for use in the OOD detection, e.g., according to method 500.
  • the method 600 may comprise, in an operation titled “ASSOCIATING MODELS WITH MAIN MODEL”, associating 630 the multiple secondary models with the main model to enable the OOD detection.
  • the operations of method 500 of Fig. 5 and method 600 of Fig. 6 may be performed in any suitable order, e.g., consecutively, simultaneously, or a combination thereof, subject to, where applicable, a particular order being necessitated, e.g., by input/output relations.
  • Some or all of the methods may also be combined, e.g., method 600 of enabling OOD detection may be successively used to perform OOD detection using method 500.
  • the method(s) may be implemented on a computer as a computer implemented method, as dedicated hardware, or as a combination of both.
  • instructions for the computer e.g., executable code
  • the executable code may be stored in a transitory or non-transitory manner. Examples of computer readable mediums include memory devices, optical storage devices, integrated circuits, servers, online software, etc.
  • Fig. 7 shows an optical disc 700.
  • the computer readable medium 700 may comprise transitory or non- transitory data 710 representing multiple secondary models.
  • the secondary models may be associated with a main model to enable OOD detection.
  • the main model may be configured to generate an output image from an input instance.
  • the main model may be trained on a training dataset.
  • the secondary models may be trained on the training dataset on which the main model is trained.
  • a secondary model may be for determining a secondary model output image for an input instance for use in the OOD detection.
  • the secondary models may be obtained according to computer- implemented 600.
  • the secondary models may be for use in computer-implemented method 500.
  • the expression, “at least one of A, B, and C” should be understood as including only A, only B, only C, both A and B, both A and C, both B and C, or all of A, B, and C.
  • the invention may be implemented by means of hardware comprising several distinct elements, and by means of a suitably programmed computer. In the device claim enumerating several means, several of these means may be embodied by one and the same item of hardware. The mere fact that certain measures are recited in mutually different dependent claims does not indicate that a combination of these measures cannot be used to advantage.

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