Original: Tactile Image-to-Image Disentanglement of Contact Geometry from Motion-Induced Shear
Revised: Tactile Image-to-Image Disentanglement of Contact Geometry from Motion-Induced Shear

Original: Abstract: Robotic touch, particularly when using soft optical tactile sensors,suffers from distortion caused by motion-dependent shear.
Revised: Abstract: Robotic touch, particularly when using soft optical tactile sensors, suffers from distortion caused by motion-dependent shear.

Original: The manner in whichthe sensor contacts a stimulus is entangled with the tactile information aboutthegeometry of the stimulus.
Revised: The manner in which the sensor contacts a stimulus is entangled with the tactile information about the stimulus geometry.

Original: In this work, we propose a supervised convolutionaldeep neural network model that learns to disentangle, in the latent space, thecomponents of sensor deformations caused by contact geometry from those dueto sliding-induced shear.
Revised: In this work, we propose a supervised convolutional deep neural network model that learns to disentangle, in the latent space, the components of sensor deformations caused by contact geometry from those due to sliding-induced shear.

Original: The approach is validated by reconstructing unshearedtactile images  from sheared images and showing they match unsheared tactileimages collected with no sliding motion.
Revised: The approach is validated by showing a close match between the unsheared images reconstructed from sheared images and their vertical tap (non-sheared) counterparts.

Original: In addition, the unsheared tactile imagesgive a faithful reconstruction of the contact geometry that is not possible from the sheared data, and  robust estimation of the contact pose that can be used forservo control sliding around various 2D shapes.
Revised: In addition, the unsheared tactile images faithfully reconstruct the contact geometry masked in sheared data, and allow robust estimation of the contact pose of use for sliding exploration of various planar shapes.

Original: Finally, the contact geometryreconstruction in conjunction withservo control sliding  were used for faithful full object reconstruction of various 2D shapes.
Revised: Overall, the contact geometry reconstruction in conjunction with sliding exploration were used for faithful full object reconstruction of various planar shapes.

Original: The methods have broad applicabilityto deep learning models for robots with a shear-sensitive sense of touch.
Revised: The methods have broad applicability to deep learning models for robots with a shear-sensitive sense of touch.

Original: [Figure]
Revised: [Figure]

Revised: (tapping) data was by the target; sheared (sliding) data was collected by sliding to the target, and (e) Schematic of the Disentangled UnshearNet model architecture with representative input/output tactile images and contact geometry reconstructions

Original:  Introduction
Revised:  Introduction

Original: A fundamental aspect of tactile sensing is that it measures the environment via physical contact.
Revised: A fundamental aspect of tactile sensing is that it measures the environment via physical contact.

Original: Therefore, the manner in which thesensor contacts a stimulus is entangled with the tactile information about that  stimulus.
Revised: This entangles the stimulus related tactile information with that induced by the manner of contact between the sensor and the stimulus.

Original: For example, when sliding or rubbing ﬁngers across tactile stimuli, soft tactile sensors are inevitably distorted by motion-dependent shear, making the sensor response history- dependent and generalization hard in tactile tasks.
Revised: For example, when sliding or rubbing ﬁngers across tactile stimuli, soft tactile sensors are inevitably distorted by motion-dependent shear, making the sensor response history-dependent and generalization hard in tactile tasks.

Original: This issue is prevalent in camera-based optical tactile sensors that use the lateral motion of markers to infer contact geometry, such as theTacTip [1],
Revised: This issue is prevalent in camera-based optical tactile sensors that use the lateral motion of markers to infer contact geometry, such as the

Original:  ChromaTouch [2], GelForce [3] and the optical tactile sensor described in [4], but may occur also in other shear-sensitive tactile sensors.
Revised: TacTip [1, 2], ChromaTouch [3], GelForce [4] and the optical tactile sensor described in [5], but may occur also in other shear-sensitive tactile sensors.

Original: Generally, this shear distortion of the sensor response when sliding along surfaces would make it difﬁcult to perform tactile-dependent tasks such as shape reconstruction and continuous object exploration or manipulation
Revised: Generally, this shear distortion of the sensor response when sliding along surfaces would make it difﬁcult to perform tactile-dependent tasks such as shape reconstruction and continuous object exploration or manipulation.

Original: Therefore, an important capability is to separate the deformation due to the manner of contact fromthat due to the stimulus geometry.
Revised: Therefore, an important capability is to separate the deformation due to the manner of contact from that due to the stimulus geometry.

Original: For example, when continuously exploring an object surface, thesliding-induced shear would need to be removed from tactile image to extract the local contact shape.
Revised: For example, when continuously exploring an object surface, the sliding-induced shear would need to be removed from tactile image to extract the local contact shape.

Original: Previous work on extracting pose information from contact to continuously slide a tactile sensor overcomplex objects used a deep convolutional neural network trained to map between shear-distortedinputs and the desired (pose) outputs, which was necessary for sliding exploration over a range ofcomplex novel objects [5, 6, 7].
Revised: Previous work on extracting pose information from contact to continuously slide a tactile sensor over complex objects used a deep convolutional neural network trained to map between shear-distorted inputs and the desired (pose) outputs, which was necessary for sliding exploration over a range of complex novel objects [6, 7, 8].

Original: Here, we suggest, an alternate disentanglement based approach thatlearns to remove motion-induced shear from raw sheared sensor response that has several advantagesover previous task-speciﬁc approach of training insensitivity to shear, in that: (a) it is computationallyand data efﬁcient by only requiring the ‘unshearing’ of the tactile data to be learnt once instead ofrelearning for each tactile task, such as when applied to full object reconstruction; (b) the modelscan then be learnt more easily on unsheared data, which we demonstrate by predicting local objectpose; moreover, in some cases no model need be learnt at all, which we demonstrate with contactsurface reconstruction using a Voronoi tessellation from the tactile marker data; and (c) the methodsare extensible to including other downstream variables of interest appropriate to the task, rather thanhaving to completely retrain new models from scratch.
Revised: Here, we suggest, an alternate disentanglement based approach that learns to remove motion-induced shear from raw sheared sensor response that has several advantages over previous task-speciﬁc approach of training insensitivity to shear, in that: (a) it is computational and data efﬁcient by only requiring the ‘unshearing’ of the tactile data to be learnt once instead of relearning for each tactile task, such as when applied to full object reconstruction (Sec. 4.4); (b) the models can then be learnt more easily on unsheared data, which we demonstrate by predicting local object pose; moreover, in some cases no model need be learnt at all, which we demonstrate with contact surface reconstruction using a Voronoi tessellation from the tactile marker data; and (c) the methods are extensible to including other downstream variables of interest appropriate to the task, rather than having to completely retrain new models from scratch.

Original: Our approach to disentangling environmental factors of variation and object attributes in tactilesensing is based on work in computer vision where disentanglement is considered important toimprove the generalizability of machine learning models, for example to aid in learning of robustobject representations for object classiﬁcation under novel scenarios [8].
Revised: Our approach to disentangling environmental factors of variation and object attributes in tactile sensing is based on work in computer vision where disentanglement is considered important to improve the generalizability of machine learning models, for example to aid in learning of robust object representations for object classiﬁcation under novel scenarios [9].

Original: Inspired from this, here wepropose a supervised convolutional neural network model that learns to disentangle the components ofsensor deformation caused by the contacted object geometry from those due to motion-induced shear.
Revised: Inspired from this, here we propose a supervised convolutional neural network model that learns to disentangle the components of sensor deformation caused by the contacted object geometry from those due to motion-induced shear.

Original: The models were trained using paired data from discrete (tapping) and continuous (sliding) touch,with an image-to-image ‘Disentangled UnshearNet’ model architecture that outputs unsheared tactileimages from sheared images (Fig. 1).
Revised: The models were trained using paired data from vertical tap (non-sheared) and continuous (sliding) touch, with an image-to-image Disentangled UnshearNet model architecture that outputs unsheared tactile images from sheared images (Fig. 1).

Original: Our validation: (1) quantiﬁes that the unsheared images fromcontinuous motion match their paired tactile images from discrete taps (Table 1); (2) demonstratesthat local contact geometry reconstructed from unsheared images using Voronoi match their pairedtapping counterparts over several stimuli shapes (Fig. 4, top row); (3) infers pose from the shearedtactile images by re-using a convolutional neural network model trained on discrete (tapping) data,which was then applied to controlling robust sliding exploration around several planar objects (Fig. 4,middle row) ; and (4) combines the two previous steps to attain faithful full-object reconstruction ofseveral planar shapes (Fig. 4, bottom row).
Revised: Our validation: (1) quantiﬁes that the unsheared images from continuous motion match their paired tactile images from discrete taps (Sec. 4.1); (2) demonstrates that local contact geometry reconstructed from unsheared images using Voronoi match their paired tapping counterparts over several stimuli shapes (Fig. 4, top row); (3) infers pose from the sheared tactile images by re-using a convolutional neural network model trained on vertical tap (non-sheared) data, which was then applied to controlling robust sliding exploration around several planar objects (Fig. 4, second row); and (4) combines the two previous steps to attain faithful full-object reconstruction of several planar shapes (Fig. 4, third row).

Original:  Background
Revised:  Background

Original: Measuring strain is a fundamental component of tactile sensing, as emphasised by Platkiewicz, etal [9]: ‘the pressure distribution at the surface of a tactile sensor cannot be acquired directly and mustbe inferred from the [strain] ﬁeld induced by the touched object in the sensor medium.’
Revised: Measuring strain is a fundamental component of tactile sensing, as emphasised by Platkiewicz, et al [10]: ‘the pressure distribution at the surface of a tactile sensor cannot be acquired directly and must be inferred from the [strain] ﬁeld induced by the touched object in the sensor medium.’

Original: There are many mechanisms whereby normal strain and shear strain are measured by tactile sensors.
Revised: There are many mechanisms whereby normal strain and shear strain are measured by tactile sensors.

Original: Taxel-based tactile sensors such as the iCub ﬁngertip [10] and BioTac [11] directly measure normalstrain.
Revised: Taxel-based tactile sensors such as the iCub ﬁngertip [11] and BioTac [12] directly measure normal strain.

Original: Nevertheless, this measurement of normal strain will be affected by shearing of the soft sensormedium, although the effects on sensor output will be much smaller than those from normal pressure.
Revised: Nevertheless, this measurement of normal strain will be affected by shearing of the soft sensor medium, although the effects on sensor output will be much smaller than those from normal pressure.

Original: Camera-based optical tactile sensors can be very sensitive to shear because they transduce deformationof the soft sensor surface into a lateral image.
Revised: Camera-based optical tactile sensors can be very sensitive to shear because they transduce deformation of the soft sensor surface into a lateral image.

Original: For optical tactile sensors such as the TacTip biomimeticoptical sensor used here [13, 1] and other marker-based sensors [2, 4], the surface shear will alsodistort the apparent geometry of the contact.
Revised: For optical tactile sensors such as the TacTip biomimetic optical sensor used here [1, 2, 14] and other marker-based sensors [3, 5], the surface shear will also distort the apparent geometry of the contact.

Original: This distortion is because the normal indentation isrepresented in the local shear strain of the markers, upon which the global shear strain is superimposed.
Revised: This distortion is because the normal indentation is represented in the local shear strain of the markers, upon which the global shear strain is superimposed.

Original: This contrasts with optical tactile sensors that reconstruct the indentation ﬁeld from reﬂection, suchas the GelSight [14], where shear will shift the imprint on the tactile image but otherwise the imprintshape should be relatively unaffected.
Revised: This contrasts with optical tactile sensors that reconstruct the indentation ﬁeld from reﬂection, such as the GelSight [15], where shear will shift the imprint on the tactile image but otherwise the imprint shape should be relatively unaffected.

Original: This effect of shear complicates tactile perception under general motions against an object, andrestricts the application of touch on challenging tasks such as tactile exploration and surface shapereconstruction.
Revised: This effect of shear complicates tactile perception under general motions against an object, and restricts the application of touch on challenging tasks such as tactile exploration and surface shape reconstruction.

Original: Studies have been limited to discrete contacts where the sensor taps discretely overthe object to minimize shear [16, 17, 19], or to rigid planar tactile sensors [20, 21] that do not shear.
Revised: Studies have been limited to discrete contacts where the sensor taps discretely over the object to minimize shear [17, 18, 20], or to rigid planar tactile sensors [21, 22] that do not shear.

Original: A recent body of work on the TacTip sensor used here focused on mitigating the effects of motiondependent shear during tactile servo control to slide around planar shapes [5, 18] and complex3D objects [6, 7].
Revised: A recent body of work on the TacTip sensor used here focused on mitigating the effects of motiondependent shear during tactile servo control to slide around planar shapes [6, 19] and complex 3D objects [7, 8].

Original: The shear-dependence problem was addressed in three studies that used a deep convolutional neural network to predict pose by training insensitivity to shear into the predictionnetwork [5, 6, 7].
Revised: The shear-dependence problem was addressed in three studies that used a deep convolutional neural network to predict pose by training insensitivity to shear into the prediction network [6, 7, 8].

Original: While effective, this has a drawback that procedures for learning shear-invarianceneeds to be introduced into the training for each individual task, and thus would not generalize easilyto new tasks.
Revised: While effective, this has a drawback that procedures for learning shear-invariance needs to be introduced into the training for each individual task, and thus would not generalize easily to new tasks.

Original: Another study did not use deep learning, but instead dimensionally reduced the tactiledata [18], where the the pose components naturally separated from the shear components.
Revised: Another study did not use deep learning, but instead dimensionally reduced the tactile data [19], where the the pose components naturally separated from the shear components.

Original: This work pursues an alternate approach using deep learning to remove the effect of motion-dependentshear from the sheared tactile image, offering several advantages that were summarized in theintroduction.
Revised: This work pursues an alternate approach using deep learning to remove the effect of motion-dependent shear from the sheared tactile image, offering several advantages that were summarized in the introduction.

Original: Our approach to disentangling environmental factors of variation and object attributesin tactile sensing is based on work in computer vision where disentanglement is considered importantto improve the generalization of machine learning models, for example to aid in learning of robustobject representations for object classiﬁcation under novel scenarios [8].
Revised: Our approach to disentangling environmental factors of variation and object attributes in tactile sensing is based on work in computer vision where disentanglement is considered important to improve the generalization of machine learning models, for example to aid in learning of robust object representations for object classiﬁcation under novel scenarios [9].

Original: Once disentangled, differentenvironmental factors and object attributes can be recombined to generate coherent novel conceptsthus extending knowledge to previously unobserved scenarios [8].
Revised: Once disentangled, different environmental factors and object attributes can be recombined to generate coherent novel concepts thus extending knowledge to previously unobserved scenarios [9].

Original: For example, synthesizing sensorresponses to novel stimuli by combining the stimuli attributes and factor of variation without actuallyobserving them to plan action under previously unobserved conditions.
Revised: For example, synthesizing sensor responses to novel stimuli by combining the stimuli attributes and factor of variation without actually observing them to plan action under previously unobserved conditions.

Original: In the case of tactile sensingconsidered here, the stimuli attributes could be novel contact geometry and the factors of variationthe motion-induced shear.
Revised: In the case of tactile sensing considered here, the stimuli attributes could be novel contact geometry and the factors of variation the motion-induced shear.

Original:  Methods 
Revised:  Methods 3.1 Experimental Setup

Original: [Figure] 3.1 Experimental Setup

Original: [Figure] The setup  in this study followed recent experiments with the TacTip biomimetic  optical tactile sensor[5, 18, 6, 7] where it is mountedas an end effector on a robot arm (Fig. 1).
Revised: The setup used in this study was similar to that previously used in [6, 7, 8, 19] where a biomimetic soft optical tactile sensor – the TacTip – was mounted on an industrial robot arm (ABB IRB120) as an end effector.

Original: The TacTip is biomimeticin that its skin morphology is based on the layered dermal and epidermal structure of the humanﬁngertip [13, 1]; the tactile sensor measures the shear displacement of an array of papillae pins on theinner side of the sensing surface caused by the skin deformation.
Revised: The sensor skin morphology mimics the layered dermal and epidermal structure of the human ﬁngertip [1, 2, 14] and encodes tactile information in the shear displacement of the papillae (marker) pins, on the inner side of the sensing surface, caused by the skin deformation.

Original: TheTacTip can be designed with varied morphologies dictated by the application [1].
Revised: The

Original: The TacTipsensor (Fig. 1 (a) & (b)) used in this work had a  soft rubber-like hemispherical dome (40 mm radius, TangoBlack+) manufactured using multi-material 3D printing. Its inner side was covered withanarray of 331  pins withhard white tips arranged in a concentric circular grid.
Revised: TacTip used in this work consisted of a 3D printed soft rubber-like hemispherical dome (40 mm radius, TangoBlack+) with its inner surface covered with 331 marker pins with white tips arranged in a concentric circular grid.

Original: The dome was ﬁlledwith an optically-clear silicone gel to give it a compliance similar toa human ﬁngertip.
Revised: The dome was ﬁlled with an optically-clear silicone gel to achieve compliance akin to human ﬁngertip.

Original: The ﬁnalassembly of sensors is done by hand that introduces variability in the response in other otherwisesame sensors.

Original: A camera was used to collect tactile images of the internal surface of the dome.
Revised: An RGB camera (ELP 1080p module) captures the inner surface of the dome.

Original: Formore details, we refer to the references above.
Revised: For more details, we refer to the references above.

Revised: The manual ﬁnal assembly of the sensor introduces minor variability in the sensor response of the otherwise similar sensors.

Original: The tactile stimuli usedhere were three 3D-printed (ABS plastic) planar shapes: a circular disk, cloverand teardrop (Fig.
Revised: For training, we used three 3D-printed (ABS plastic) planar shapes: a circular disk, clover and teardrop shown in Fig.

Original: 1 (c)).
Revised: 1 (c) (red circles show the approximate location of data collection).

Original: These objects were chosen to give different edge shapes for applicationof our methods, and were fastened securely to the workspace to prevent accidental motion. Anadditional four complex planar shapes, including two acrylic shapes with distinct frictional propertiesto the remaining 3D-printed shapes (spiral 1 & 2, Fig. 4) were used to test for generalizability.
Revised: For testing, we used sever planar shapes with various morphologies including two acrylic shapes with distinct frictional properties to the other ﬁve 3D-printed shapes (Fig. 4, second row). All shapes were securely fastened to the workspace to prevent accidental motion.

Original: 3.2 Data Collection 
Revised: 3.2 Data Collection 3.2.1 Paired Canonical and Sheared Data

Original: 3.2.1 Paired Canonical and Sheared Data

Original: This work proposes a supervised deep learning model Disentangled UnshearNet to remove the effectof motion-induced global shear in the tactile images, caused by the friction between the sensor skinand its contacted surface during contact.
Revised: This work proposes a supervised deep learning model Disentangled UnshearNet to remove the effect of motion-induced global shear in the tactile images, caused by the friction between the sensor skin and its contacted surface during contact.

Original: We emphasise this motion-induced shear is different fromthe skin deformation due to local shear from the geometry of the stimulus imprint.
Revised: We emphasise this motion-induced shear is different from the skin deformation due to local shear from the geometry of the stimulus imprint.

Original: Our method requires paired tactile data with minimal global shear taken from vertically tapping ontothe stimulus (referred to as canonical data) and sliding data with random global shear (referred to assheared data).
Revised: Our method requires paired tactile data with minimal global shear taken from vertically tapping onto the stimulus (referred to as canonical data) and sliding data with random global shear (referred to as sheared data).

Original: The sheared data is collected after sliding randomly and is paired with a tactile imagefrom the canonical data by using the same relative poses between the sensor and the stimuli (Fig. 1).
Revised: The sheared data is collected after sliding randomly and is paired with a tactile image from the canonical data by using the same relative poses between the sensor and the stimuli (Fig.(d)).

Original: The raw tactile data was cropped, sub-sampled to a 256 × 256-pixel region and ﬁnally converted tobinary images using an adaptive threshold to minimise sensitivity to internal lighting conditions.
Revised: The raw tactile data was cropped, sub-sampled to a 256 ⇥ 256-pixel region and ﬁnally converted to binary images using an adaptive threshold to minimise sensitivity to internal lighting conditions.

Original: In total, data for 200 distinct poses were collected for each of the three  stimuli (Fig.
Revised: In total, data for 200 distinct poses were collected for each of the three training stimuli (Fig.

Original: 1 (c)).
Revised: 1 (c)).

Original: To generateposes, the sensor location relative to the target contact location (red circle, Fig.
Revised: To generate poses, the sensor location relative to the target contact location (red circle, Fig.

Original: 1 (d)) was sampledrandomly from a uniform distribution spanning the range 5, 5] mm in the two lateral [-directions(along the x - and y -axes), [-45, -45]
Revised: 1 (d)) was sampled randomly from a uniform distribution spanning the range directions (along the x - and y -axes), [-45, -45]

Original: deg in yaw ( θ n Z ) and
Revised: deg in yaw ( q n Z ) and

Original: mm in depth ( z -axis).Ranges of [Figure] [Figure]
Revised: mm in depth ( z -axis).

Original: L2 Loss

Original: Encoder (E)

Original: Decoder (D)

Original: Patch Loss

Original: L

Original: [Figure]

Original: C

Original: PC

Original: [-PC C 
 [Figure]-] the target poses and perturbations to generate canonical and sheared data were chosen to ensure safecontact of the sensor with the stimulus (Fig.
Revised: [-PC C 
 [Figure]-]Ranges of the target poses and perturbations to generate canonical and sheared data were chosen to ensure safe contact of the sensor with the stimulus (Fig.

Original: 1 (c)).
Revised: 1 (c)).

Original: Canonical Data: The canonical data was taken by vertically tapping onto the stimulus, to give arepresentative sample of tactile data with minimal global shear just due to the stimulus geometry.
Revised: Canonical Data: The canonical data was taken by vertically tapping onto the stimulus, to give a representative sample of tactile data with minimal global shear just due to the stimulus geometry.

Original: This gives target (reference) data that the sheared data from sliding contacts should be restored to.
Revised: This gives target (reference) data that the sheared data from sliding contacts should be restored to.

Original: The dataset, in total, had 30,000 samples: 50 instances of each of the 200 poses recorded previouslyfor each of the three stimuli shapes (Fig.
Revised: The dataset, in total, had 30,000 samples: 50 instances of each of the 200 poses recorded previously for each of the three stimuli shapes (Fig.

Original: 1 (c)).
Revised: 1 (c)).

Original: To generate instances, the indentation depth ( z -axes)was varied randomly between [-1, 1] mm from the original indentation depth.
Revised: To generate instances, the indentation depth ( z -axes) was varied randomly between [-1, 1] mm from the original indentation depth.

Original: Sheared Data: The sheared data accords to a canonical tactile image distorted by global shear fromlateral sliding motion of the sensor on the stimulus.
Revised: Sheared Data: The sheared data accords to a canonical tactile image distorted by global shear from lateral sliding motion of the sensor on the stimulus.

Original: Thus, the sheared data does not give contact-onlyinformation akin to canonical data that represented the geometry of the contacted stimulus, but has asigniﬁcant component due to the contact motion.
Revised: Thus, the sheared data does not give contact-only information akin to canonical data that represented the geometry of the contacted stimulus, but has a signiﬁcant component due to the contact motion.

Original: The dataset, in total, had 90,000 samples: 150 instances of each of the 200 random poses recordedpreviously for each of the three stimulus shapes (Fig.
Revised: The dataset, in total, had 90,000 samples: 150 instances of each of the 200 random poses recorded previously for each of the three stimulus shapes (Fig.

Original: 1 (c)).
Revised: 1 (c)).

Original: To generate instances for each pose, thelateral position offset for sliding to the target pose was varied randomly between 2.5, 2.5] mm [-inlateral direction(s) (along the x - or y -axes or both), using the procedure shown in Fig.
Revised: To generate instances for each pose, the lateral position offset for sliding to the target pose was varied randomly between in lateral direction(s) (along the x - or y -axes or both), using the procedure shown in Fig.

Original: 1 (d).
Revised: 1 (d).

Original: Training and Test Data: The canonical and sheared datasets were partitioned randomly into training,validation and test sets (ratio 60:20:20); i.e. from the 200 unique poses for each stimulus shape (Fig. 1(c)), 120 poses were assigned to a training set and 40 poses each to validation and testing sets.
Revised: Training and Test Data: The canonical and sheared datasets were partitioned randomly into training, validation and test sets (ratio 60:20:20); i.e. from the 200 unique poses for each stimulus shape (Fig.(c)), 120 poses were assigned to a training set and 40 poses each to validation and testing sets.

Original: Overallthe canonical and sheared training set contained 18,000 and 54,000 samples respectively, while thevalidation and testing sets contained 6,000 and 18,000 samples respectively.
Revised: Overall the canonical and sheared training set contained 18,000 and 54,000 samples respectively, while the validation and testing sets contained 6,000 and 18,000 samples respectively.

Original: To generate pairedcanonical and transformed data for training, each transformed tactile image was paired randomlywith one of the canonical instances having the same pose.
Revised: To generate paired canonical and transformed data for training, each transformed tactile image was paired randomly with one of the canonical instances having the same pose.

Original: 3.2.2 Pose-labelled Data
Revised: 3.2.2 Pose-labelled Data

Original: To train pose prediction network PoseNet , a separate set of pose data was collected instead of reusingthe previously collected pose data to train Entangled & Disentagled UnshearNet .
Revised: To train pose prediction network PoseNet , a separate dataset was collected instead of reusing the dataset used to train Entangled & Disentagled UnshearNet .

Original: This was doneto not overﬁt the training set andto ensure performance of the trained UnshearNet models despitepotential dataset shifts due to a host of factors, including drift in sensor characteristics over time orwith continued use due to wear and tear of the tactile sensing surface.
Revised: This was done to prevent the model from overﬁtting the training set and ensure performance of the trained UnshearNet models despite potential dataset shifts due to a host of factors, including drift in sensor characteristics over time or with continued use due to wear and tear of the tactile sensing surface.

Original: The dataset had, in total, 30,000 samples: 10,000 samples from each of the three  object shapes(Fig.
Revised: The dataset had, in total, 30,000 samples: 10,000 samples from each of the three training object shapes (Fig.

Original: 1 (c)).
Revised: 1 (c)).

Original: To generate contact poses, the sensor location relative to the initial contact location wassampled randomly from a uniform distribution spanning the range 5, 5] mm laterally ( x - and y [--axisdirections), [-45, -45]
Revised: To generate contact poses, the sensor location relative to the initial contact location was sampled randomly from a uniform distribution spanning the range -axis directions), [-45, -45]

Original: deg in yaw ( θ n Z ) and
Revised: deg in yaw ( q n Z ) and

Original: mm in depth ( z -axis).
Revised: mm in depth ( z -axis).

Original: Ranges of the target poses,as before, were chosen to ensure safe contact of the sensor without causing damage.
Revised: Ranges of the target poses, as before, were chosen to ensure safe contact of the sensor without causing damage.

Original: As discussedabove, all tactile images were cropped, sub-sampled and thresholded to 256 × 256-pixel to binary(black/white) tactile images.
Revised: As discussed above, all tactile images were cropped, sub-sampled and thresholded to 256 ⇥ 256-pixel to binary (black/white) tactile images.

Original: The dataset was partitioned randomly into training , validation and testsets in the ratio 60:20:20 as above, containing 18,000, 6,000 and 6,000 samples respectively. 
Revised: The dataset was partitioned randomly into training , validation and test sets in the ratio 60:20:20 as above, containing 18,000, 6,000 and 6,000 samples respectively. [Figure] L [Figure]

Revised: [Figure]

Revised: [Figure]

Original: 3.3 Image-to-Image Models for Shear Removal
Revised: 3.3 Image-to-Image Models for Shear Removal

Original: To achieve our goal of removing the effects of shear induced by the sliding motion, we trained twomodels based on the encoder-decoder framework – Entangled UnshearNet (Fig. 2) and Disentangled
Revised: To achieve our goal of removing the effects of shear induced by the sliding motion [Figure] we trained two models based on the encoder-decoder framework – Entangled UnshearNet (Fig. 2) and Disentangled

Original: UnshearNet (Fig. 3).
Revised: UnshearNet (Fig. 3).

Original: The former model (baseline) learns the mapping between the input sheared dataand its corresponding canonical (tap) data directly.
Revised: The former model (baseline) learns the mapping between the input sheared data and its corresponding canonical (tap) data directly.

Original: The later model instead, ﬁrst disentangles thecontact-only (pose) sensor response component from the sliding-induced global shear component inthe latent space of the encoder E ; followed by accurate reconstruction of the input sheared image andits corresponding canonical (tap) image using decoders DS (sheared or sliding) and DC (canonical ortapping).
Revised: The later model instead, ﬁrst disentangles the contact-only (pose) sensor response component from the sliding-induced global shear component in the latent space of the encoder E ; followed by accurate reconstruction of the input sheared image and its corresponding canonical (tap) image using decoders DS (sheared or sliding) and DC (canonical or tapping).

Original: We hypothesized that a more robust mapping between sheared and canonical (tap) datacan be learned by disentangling the contact-only and sliding-induced components of sensor response.
Revised: We hypothesized that a more robust mapping between sheared and canonical (tap) data can be learned by disentangling the contact-only and sliding-induced components of sensor response.

Original: The mathematical formulation of the Disentangled UnshearNet is listed below:
Revised: The mathematical formulation of the Disentangled UnshearNet is listed below

Original:  The encoder E splits the latent space into two components z = ( z p , z s ) ∈{+
+}
Revised: : The encoder E splits the latent space into two components z = ( z p , z s ) {+
+}

Original: Z p × Z s , given paired canonical { x c } Ni = 1 and shear-transformed training samples { x s } Ni = 1 , where x c ∈ X c and x s ∈ X s are in the sets of canonical and sheared data, respectively.
Revised: Z p ⇥ Z s , given paired canonical { x c } Ni = 1 and shear-transformed training samples { x s } Ni = 1 , where x c 2 X c and x s 2 X s are in the sets of canonical and sheared data, respectively.

Original: The decoder DC takes as input only the pose part of the latent code z p and reconstructs the canonical sample corresponding to the input sheared sample.
Revised: The decoder DC takes as input only the pose part of the latent code z p and reconstructs the canonical sample corresponding to the input sheared sample.

Original: In combination with the encoder E , it thus learns 
Revised: In combination with the encoder E , it thus learns a mapping M : X t !

Original: a mapping M : X t → X c from the sheared to canonical data.
Revised: X c from the sheared to canonical data.

Original: The other decoder DS , takes as input the full latent code z and reconstructs the input sheared sample.
Revised: The other decoder DS , takes as input the full latent code z and reconstructs the input sheared sample.

Original: In combination with the encoder E , it thus acts as an auto-encoder and learns a mapping N : X s → X sfrom the sheared data to itself.
Revised: In combination with the encoder E , it thus acts as an auto-encoder and learns a mapping N : X s ! X s from the sheared data to itself.

Original: Our objective function has three components:
Revised: Our objective function has three components:

Original: (1) L2 loss for matching the generated canonical samples M ( x t ) to their targets x c ;(2) L1 patch loss for matching random patches extracted from generated canonical images M ( x t ) andcorresponding targets x c for enforcing image similarity locally as changes in sensor response due tochange in contact conditions are predominately local in nature;(3) Reconstruction loss for matching the generated sheared samples N ( x t ) to their target input shearedsamples x s .
Revised: (1) L2 loss for matching the generated canonical samples M ( x t ) to their targets x c ; (2) L1 patch loss for matching random patches extracted from generated canonical images M ( x t ) and corresponding targets x c for enforcing image similarity locally as changes in sensor response due to change in contact conditions are predominately local in nature; (3) Reconstruction loss for matching the generated sheared samples N ( x t ) to their target input sheared samples x s .

Original: The objective functions are:
Revised: The objective functions are:

Original: [Equation]
Revised: [Equation]

Original: ) where ( z p , z s ) =
Revised: where ( z p , z s ) =

Original: E ( x s ) for all x s ∈ X s .
Revised: E ( x s ) for all x s 2 X s .

Original: The function crops () selects a patch of size 20 × 20 pix from
Revised: The function crops () selects a patch of size 20 ⇥ 20 pix from

Original: M ( x t ) and x c .
Revised: M ( x t ) and x c .

Original: The objective functions L rec , L sup and L patch represent sheared reconstruction loss,canonical supervised loss and canonical supervised patch loss respectively.
Revised: The objective functions L rec , L sup and L patch represent sheared reconstruction loss, canonical supervised loss and canonical supervised patch loss respectively.

Original: The ﬁnal objectives for Encoder E and Decoders DC , DS are:
Revised: The ﬁnal objectives for Encoder E and Decoders DC , DS are:

Original: [Equation]
Revised: [Equation]

Original: 6) where λ is the relative loss scale factor.
Revised: where l = 0.1 is the relative loss scale factor.

Original: Details of the speciﬁc model architectures and their training are given in Appendices A & B.
Revised: Details of the speciﬁc model architectures and their training are given in Appendices A & B.

Original:  Experimental Results4.1 Shear Removal from Tactile Images
Revised:  Experimental Results 4.1 Shear Removal from Tactile Images

Original: We ﬁrst performed an ablation study to demonstrate the separation of latent representations by the
Revised: We ﬁrst performed an ablation study to demonstrate the separation of latent representations by the

Original: Disentangled UnshearNet into pose and shear codes respectively.
Revised: Disentangled UnshearNet into pose and shear codes respectively.

Original: For details see Appendix D.
Revised: For details see Appendix D.

Original: The ﬁrst test of the performance of our approach for removing motion-induced global shearfromtactile images usedthe multi-scale structural similarity index (SSIM) [25] to compare tactile imagesfrom the shear-transformed test data set with the paired canonical and the Disentangled (Entangled) UnshearNet -generated unsheared tactile images.
Revised: The ﬁrst test of the effectiveness of our approach in removal of motion-induced global shear used multi-scale structural similarity index (SSIM) [26] to compare image similarity between Disentangled (Entangled) model-generated unsheared images PC and their test set sheared S and canonical (nonsheared) C counterparts.

Original: All three images represent the same pose. To compare, we computed the average SSIM between the canonical (tap)-sheared and canonical(tap)-unsheared images in several distinct scenarios (stimuli: disk edge, clover corner, teardropcorner). The unsheared images were structurally closer to the target canonical (tap) samples than theirsheared counterparts. The overall SSIM value for unsheared samples was 0.93 (0.90) in comparisonto 0.32 for sheared samples, with closeness to unity indicating a good match (Table 1).
Revised: On comparison, we found the Disentangled / Entangled UnshearNet model generated unsheared images PC to be structurally closer to the target canonical images C (93% / 90%) than their sheared S counterparts (32%).

Original: Performancewas similar for all stimuli considered with Disentangled UnshearNet achieving closer match tocanonical samples than its Entangledcounterpart.
Revised: This clearly shows that our model Disentagled UnshearNet performed better in removing global shear from tactile images vis-´a-vis the baseline model Entangled

Original: [Table]
Revised: UnshearNet .

Original: 4.2 Reconstructed Contact Geometry
Revised: 4.2 Reconstruction of Local Contact Geometry

Original: As stated in the introduction, an application of shear  removalis to aid reconstruction of the stimulusgeometry fromthe tactile images.
Revised: Motion-induced global shear masks the contact geometry necessitating removal of shear from tactile images to reconstruct true indentation ﬁeld (Fig. 4, top row).

Original: This is validated by using a Voronoi-based methodto infer anapproximate indentation ﬁeld, using the method introduced in Cramphorn et al [12] on tactile datafrom the TacTip.
Revised: We used a Voronoi-based method introduced in Cramphorn et al [13] to reconstruct indentation ﬁeld from tactile data encoded by TacTip.

Original: The Voronoi method transforms the displacements of the tactile markers  into areasof hexagonal cells tessellating the grid of the markers [12, Fig. 4].
Revised: It transforms the displacements of the tactile markers on the inner side of sensing surface into areas of hexagonal cells tessellating the grid of the markers [13, Fig. 4].

Original: The change in Voronoi  areas ofthe cells represents the  skin distortion, which correlates with the indentation due to contact geometry.
Revised: The change in Voronoi cell areas from an undeformed reference represent the magnitude of local skin distortion caused by contact, which correlates with the indentation due to contact geometry.

Original: For display purposes, we ﬁt a 3D surface to the ( x , y ) centroid coordinates using the Voronoi cell areasas the corresponding height values (Fig. 4, top row).
Revised: For display, we ﬁt a 3D surface to the ( x , y ) centroid coordinates using the Voronoi cell areas as the corresponding height values (Fig. 4, top row).

Original: The ﬁtted surface from the original canonicaltactile images taken under tapping visibly represents the shape of the indentation on the tactile sensor,as expected (Fig. 4, top row).
Revised: The ﬁtted surface to test set sheared data S is visibly distorted by shear (Fig. 4, top row).

Original: The same stimulus under sliding motion is visibly distorted byshear,resulting in an indentation ﬁeld that does not resemble the stimulus shape (Fig. 4, top row). Evidently, the indentation ﬁelds reconstructed from the model-generated unsheared tactile imagesunder sliding motion resemble those from the canonical data (Fig. 4, top row; last , all stimuli)
Revised: However, once the global shear is removed successfully by

Original: Disk Spiral Spiral 
Revised: Spiral 1 Disk

Original: Star
Revised: Star

Original: Clover
Revised: Clover

Original: Volute
Revised: Volute

Original: Teardrop
Revised: Teardrop

Revised: Spiral

Original: U n s h e a r e d ( E n t a n g l e d ) U n s h e a r e d
Revised: U n s h e a r e d ( E n t a n g l e d ) U n s h e a r e d

Original: ( D i s e n t a n g l e d ) T a p
Revised: ( D i s e n t a n g l e d ) T a p

Original: S h e a r e d
Revised: S h e a r e d

Original: U n s h e a r e d ( E n t a n g l e d ) U n s h e a r e d
Revised: U n s h e a r e d ( E n t a n g l e d ) U n s h e a r e d

Original: ( D i s e n t a n g l e d ) T a p
Revised: ( D i s e n t a n g l e d ) T a p

Original: S h e a r e d
Revised: S h e a r e d

Original: U n s h e a r e d ( E n t a n g l e d ) U n s h e a r e d
Revised: U n s h e a r e d ( E n t a n g l e d ) U n s h e a r e d

Original: ( D i s e n t a n g l e d ) T a p
Revised: ( D i s e n t a n g l e d ) T a p

Original: S h e a r e d
Revised: S h e a r e d

Revised: Disentagnled UnshearNet in model-generated unsheared images PC , the ﬁtted surface closely matches with the true representation of the indentation ﬁeld obtained from the canonical (non-sheared / tap) data C (Fig. 4, top row).

Revised: Also clear from Fig.

Revised: 4 (top row) that our model Disentangled UnshearNet is more effective in removing global shear vis-´a-vis the baseline model Entangled UnshearNet .

Original: 4.3 Validation on Shape Exploration
Revised: 4.3 2D Sliding Shape Exploration

Original: To further conﬁrm that our modelcan remove shear from transformed images we trained a predictionnetwork (PoseNet) on stimulus pose parameters: lateral position ( x -horizontal, τ X ) and in-planeorientation (yaw, θ n Z ), using canonical tactile images from vertical tapping contacts. PoseNetperformance was quantiﬁed with the mean-absolute error (MAE) between  predicted pose  and targetwhen input data were canonical, sheared  and model-generated unsheared tactile images respectivelyusing both the entangled and disentangled networks (results in Table 2).
Revised: We further conﬁrmed the performance of our model on removing global shear by computing the mean-absolute error (MAE) between the predicted pose (lateral position t X and in-plane orientation q n Z ) from Disentangled / Entangled UnshearNet generated unsheared images PC , sheared images S and canonical (non-sheared / tap) images C and the target pose using PoseNet trained only on canonical (non-sheared / vertical tap) images (Table 1).

Original: On  the sheared data, thelowest prediction error was obtained on unsheared samples with the disentangled network, withthe entangled network about 50%higher, and  on the original sheared samples about 5 × poorer.
Revised: On comparison, the lowest prediction error was found on unsheared samples obtained using disentangled network. The error increased by as much as 50% and 5 ⇥ higher on unsheared samples from entangled network and original sheared samples respectively.

Original: Again, the UnshearNet  managed to successfully correct the distortion in sensor response cause byslide-induced global shear, with the disentangled representation giving the best performance. 
Revised: Again, the UnshearNet models managed to successfully correct the distortion in sensor response cause by slide-induced global shear, with the disentangled representation giving the best performance. [Table]

Original: Another application of shear removal that also tests the real-time performance of UnshearNet is to usethe above pose prediction network to servo control smoothly over varied object shapes during slidingmotion.
Revised: To test the real-time performance and model generalizability to novel stimuli, we used PoseNet for sliding exploration of several planar shapes (Fig. 4, second row).

Revised: This testing included four additional planar shapes absent from training including two acrylic shapes that differed in frictional properties from the other 3D printed stimuli (spirals 1 & 2, Fig. 4, second row).

Original: The robot successfully traced contours across all three shapes by a combination of the use of
Revised: The robot successfully traced contours across all stimuli shapes (Fig. 4, second row) using a combination of Disentangled

Original: UnshearNet for global shear removal, PoseNet for prediction of object pose from  unsheared images(Fig. 4, second row) and a simple  control policy (see Appendix C).
Revised: UnshearNet for global shear removal, PoseNet for prediction of object pose from model-generated unsheared images and a simple servo control policy (see Appendix C).

Original: This clearly indicates that theproposed Disentangled UnshearNet is well suited for correcting the sliding-induced shear-distortedsensor response for real-time servo control applications.
Revised: This clearly indicates that the proposed Disentangled UnshearNet is well suited for correcting the sliding-induced shear-distorted sensor response for real-time servo control applications.

Original: 4.4Full Object  Reconstruction
Revised: 4.4 Object Shape Reconstruction

Original: As a ﬁnal demonstration of our model’s utility to remove shear, we reconstructed full object shapesby combined use of contact geometry estimation (section 4.3) and sliding shape exploration (section4.4), both of which are adversely affected by motion-induced shear (Fig. 4, bottom row).
Revised: As a ﬁnal test of our model’s utility to remove shear, we reconstructed full object shapes by combined use of contact geometry estimation (Sec. 4.3) and sliding shape exploration (Sec. 4.4), both tasks adversely affected by motion-induced shear (Fig. 4, third row).

Original: [Table]

Original: To attain full object reconstructions, we fused together the contact information extracted fromunsheared images corresponding to sliding contacts (acquired during shape exploration) and linearlyinterpolated them over a rectangular grid (Fig. 4, bottom row).
Revised: To attain full object reconstructions, we fused together the contact information extracted from unsheared images corresponding to sliding contacts (recorded during shape exploration) and linearly interpolated them over a rectangular grid (Fig. 4, third row).

Original: These results clearly demonstratesthe effectiveness of our approach in learning the sheared-unsheared mapping that can then later bereused for multiple downstream tasks.
Revised: These results clearly demonstrate the effectiveness of our approach in learning the sheared-unsheared mapping that can then later be reused for multiple downstream tasks.

Original: In addition, the faithful shape reconstructions along with theshape exploration across multiple  planar objects show that the model  generalizes to novel situations.
Revised: In addition, the faithful shape reconstructions along with the shape exploration across multiple novel planar objects show that the model successfully generalizes to novel situations.

Original:  Conclusion
Revised:  Discussion

Original: In this work, we proposed atactile image-to-image supervised convolutional neural network model toremove the effects of motion-induced global shear from the tactile sensor response  while preservingthe sensor deformations due to the spatial geometry of the contacted stimuli.
Revised: This work proposed a supervised approach to remove the distortion in sensor response caused by motion-induced global shear while preserving sensor deformations induced by the spatial geometry of the contacted stimuli.

Original: Two UnshearNet modelswere considered: one based on a basic encoder-decoder structurewith an entangled pose and shearlatent space, and a second that disentangled these components in themodel latent space (Figs 2, 3). 
Revised: The proposed approach was based on an encoder-decoder structure and learned to remove shear from tactile images by disentangling the pose (contact only) and shear in the latent space (Fig. 3). The disentanglement of sensor components contributed due to contact only and global shear promoted learning of robust sheared-unsheared mapping as demonstrated by better performance of this approach vis-´a-vis the baseline (Fig. 2).

Original: This approach was validated in three ways: (1) Comparing similarity of tactile images collected byvertically tapping without a shearing motion to those collected with an unknown shearing perturbation,for which the unsheared data passed through the Disentangled UnshearNet gave a good matchaccording to the structural similarity index (Table 1).
Revised: This approach was validated by: (1) demonstrating a good match (93%) between model-generated unsheared images (from sliding contacts) and its canonical (non-sheared / vertical tap) counterparts using structural similarity index measure (Sec 4.1).

Original: (2) Reconstructing the indentation ﬁeld fromthe contact geometry using sheared tactile images passed through the Disentangled UnshearNet(Fig. 4, top row), via a (Voronoi) method used previously to reconstruct the sensor deformation [12].
Revised: (2) faithful reconstruction of contact geometry, masked in sheared images, from model-generated unsheared images (Fig. 4, top row).

Original: The removal of motion-induced shear was apparent in the model-generated unsheared tactile images,with the contact geometry only visible after use of the UnshearNet with the original sheared imageobscuring the contact shape. (3) Predicting the localpose of part of an object in a shear-insensitivemanner with a prediction network trained only on canonical (tapping) data (Table 2).
Revised: (3) predicting the local object pose from model-generated unsheared images with a prediction network trained only on canonical (non-sheared / vertical tap) data (Table 1).

Original: This approachwas then applied to smooth servo control around several planar objects (Fig. 4, middle row).
Revised: This was later used for successful sliding exploration of several planar objects (Fig. 4, second row).

Original: The combination of smooth servo control and local shape reconstruction was later used for full objectreconstruction (Fig. 4, middle row), which remains an problem under active investigation in theﬁeld [23, 24].
Revised: 4) combining contact geometry reconstruction and sliding exploration to reconstruct full object shapes for several planar objects (Fig. 4, third row) which remains an problem under active investigation in the ﬁeld [24, 25].

Original: Our approach improves upon related work [5, 6] that instead trained insensitivity toshear into the prediction network itself.
Revised: Our approach improves upon related work [6, 7] that instead trained insensitivity to shear into the prediction network itself.

Original: An obvious drawback of this approach, even though it workswell for smooth servo control, is that it does not extend readily to predict other tactile dimensions suchas parameters of the local contact geometry.
Revised: While effective, this approach does not extend readily to predict other tactile dimensions such as parameters of the local contact geometry.

Original: In that case, new labelled data would need collectingto train a new model for each intended task.
Revised: In that case, new labelled data would need collecting to train a new model for each intended task.

Original: Our approach, of shear removal from tactile images,instead means that a single model based on the canonical (tapping) data can be re-used.
Revised: Our approach, of shear removal from tactile images, instead means that a single model based on the canonical (tapping) data can be re-used.

Original: The present study  considered only planar objects in 2D and two components of pose.
Revised: The current study has several limitations: 1) considered only planar objects.

Original: As recentresults have shown how to extend the PoseNet to  3D surfaces (3 pose components) or 3D edges (5pose components) for tactile servo control [5, 6], we expect the present results will extend to thosesituations, although questions remain on the best way to do this with the large number of degreesof freedom.
Revised: We, however, expect it to extend readily to to 3D objects similar to recent results that have successfully extended PoseNet to complex 3D surfaces (3 pose components) and 3D edges (5 pose components) for sliding exploration [6, 7]. 2) tested only on TacTip optical tactile sensor.

Original: Although the proposed disentanglement-based approachto remove shear from sensorresponse has been tested on TacTip optical tactile sensor, it should hold well for other soft opticalsensors. The models, however, would have to be retrained as the sensor response depends on thefrictional and elastic properties of the tactile surface, which varies across sensor types.
Revised: The approach should hold well for other soft optical sensors although difference in frictional and elastic properties between different sensor types will necessitate retraining of models.

Original: One limitation of our current approach is that we limited our training  tojust translation shear. However,smooth servoing over the objects necessarily introduces rotational shear, as the servo control rotatesthe sensor  whilecontinuously sliding over the object surface.
Revised: 3) training was limited to translation shear even though servo control introduces rotational shear due to sensor rotation while sliding over objects.

Original: However, the fact that the methodsperformed well both in controlling the sensor and reconstructing the object geometry  in the presenceof this rotational shear shows that some unshearing carries over from translation to rotational shear atleast for planar objects.
Revised: The fact that the methods worked well both for sliding exploration and contact geometry reconstruction even in absence of explicit compensation for rotational shear, shows that some unshearing carries over from translation to rotational shear at least for planar objects.

Original: Our expectation is that bringing rotational shear into the training will becomeimportant when extending the methods to 3D objects.
Revised: Our expectation is that bringing rotational shear into the training will become important when extending the methods to 3D objects.

Original: Another limitation of the supervised approachinvestigated here is the requirement of paired canonical and sheared data, which complicates thedata collection.
Revised: and 4) requires paired canonical and sheared data, which complicates the data collection.

Original: Thus, a semi-supervised approach  would be a worthwhile extension to this work, byobviating the need for paired data collection.
Revised: An approach that is more economical with labelled data requirements would be a worthwhile extension of the current work.

Original: Overall, we expect the methods developed here cancan be applied more widely to various other exploration and manipulation tasks involving soft tactilesensors that are adversely affected by motion-induced shear.APPENDIXA: Network Architectures
Revised: Overall, we expect the methods developed here can can be applied more widely to various other exploration and manipulation tasks involving soft tactile sensors that are adversely affected by motion-induced shear.

Original: Entangled UnshearNet: The encoder E compresses the input 256 × 256-pixel tactile image usingﬁve convolutional (Conv) layers, each followed by batch normalization (BN) and rectiﬁed linearunit (ReLU) activation layers respectively (architecture in Fig. 2).

Original: The output of the last Conv layer(8 × 8 × 64) is passed to the decoder D which upsamples it to an output 256 × 256-pixel canonicalimage PC .

Original: Similarly to the Conv layers, all transposed convolutional layers (T-Conv) were followedby BN and ReLU activation layers except the output layer which used sigmoid activation functioninstead (see also Fig. 2).

Original: This model was used as a baseline to evaluate the performance of proposed Disentangled UnshearNetmodel on its effectiveness in removing distortion in sensor response caused by sliding-induced globalshear.

Original: For details of the training, please see Appendix B.

Original: Disentangled UnshearNet: The encoder has the same inputs and architecture as the Entangled

Original: UnshearNet , except the the output of the 5 th Conv layer is followed by two additional Conv layers,one each for the two latent codes: Pose (8 × 8 × 64) and Shear (8 × 8 × 64). One decoder DC takes as input pose latent code and upsamples it to 256 × 256-pixel canonical outputtactile image PC . All T-Conv layers were followed by BN and ReLU activation layers except theoutput layer which used sigmoid activation layer instead (architecture shown in Fig. 3). The other decoder DS takes as input both pose and shear codes, merges them and upsamples to anoutput 256 × 256-pixel sheared image PS (intended to match the encoder input).
Revised: Acknowledgements

Original: Apart from the abovedifferences, DS has the same architectures as DC .

Original: For details of the training, please see Appendix B.

Original: PoseNet:

Original: This model takes as input 256 × 256 image, compresses it to extract features using the

Original: Conv part which are then combined using fully connected (FC) part to predict continuous-value posecomponents at the output.

Original: In total, the network consists of ﬁve convolution layers, two max pooling(MP) layers following 2 nd and 4 th Conv layers; the CONV layers were followed by BN and ReLUactivation layers respectively.

Original: The 1 st FC layer used ReLU activation while the output FC layer usedsigmoid activation.

Original: For details of the architecture and training see Fig. 5 and Appendix B. [Figure] B: Training Details
Revised: Anupam Gupta and Nathan Lepora were supported by a Research Leadership Award from the

Original: All the inputs (binary 256 × 256-pixel images) and outputs (binary 256 × 256-pixel images forimage-to-image models, pose parameters for image-to-pose model) were scaled to the range [ 0 , 1 ] .

Original: All networks weights were initialized from a zero-centered normal distribution with 0.02 standarddeviation.

Original: Both image-to-image models were trained on data collected from all three stimuli shapes(Fig.

Original: 1 (c)) as discussed in section 3.2.

Original: For image-to-image models, we used a batch size of 32.

Original: All convolutional/transposed convolutionallayers used L1/L2 regularization (10e-4) along with random image shifts, 1-2% of image size toprevent overﬁtting.

Original: The L2 loss computed across the entire image and L1 patch loss – computedbetween 100 random crops of size 20 × 20 of generated unsheared images and correspondingcanonical images – were used to train the networks in the ratio 10:1.

Original: In case of Disentangled

Original: UnshearNet , the encoder (E) and shear decoder (DS) were trained using reconstruction loss.

Original: For image-to-pose model, we used a batch size of 256.

Original: Like image-to-image models, all layersused L1/L2 regularization (10e-4) along with random image shifts, 1-2% of image size to preventoverﬁtting.

Original: The network was trained via the L2 loss computed between predicted and target poseparameters.

Original: We used ADAM optimizer [22] with learning rate of 0.0001, β 1 = 0.5 and β 2 = 0.999.

Original: We usedlearning rate scheduling for training.

Original: For image-to-image models, the learning rate was reduced toone-ﬁfth and one-tenth after 40 and 80 epochs.

Original: The models were trained, in total, for 100 epochs.

Original: Forimage-to-pose model, the learning rate was reduced to half and one-tenth after 100 and 200 epochsrespectively.

Original: The model was trained for 250 epochs.

Original: For all models, the model with best validationaccuracy was used for testing.

Original: Finally, training and optimization of the networks was implemented in the Tensorﬂow 2.0 library ona NVIDIA GTX 1660 (6 GB memory) hosted on a Ubuntu machine.

Original: C: Control Policy for Continuous Contour Following

Original: Local pose estimation allows a robot to maintain contact while safely moving over the object, thusenabling complex robot-object interactions. To demonstrate continuous 2D contour following, weused a simple control policy with following two aims: 1) keep the sensor normal to object surfacewhile in motion and 2) at every time step t , move the sensor tangentially along the surface by apredeﬁned step (0.5 mm in this case). To achieve these aims, a discrete-time proportional-integral(PI) controller was implemented to output a change in the pose of the sensor ( ∆ p ( t ) ) in its referenceframe [Equation]
Revised: Leverhulme Trust on ‘A biomimetic forebrain for robot touch’ (RL-2016-39)

Original: where K p and K i are diagonal gain matrices with proportional gain of 0.5 and integral gains of 0.3 and0.1 for translations and rotations respectively.

Original: e was error between the predicted pose and a referencenormal to the edge.

Original: D: Disentanglement of Latent Representations

Original: An ablation study was used to verify the separation of latent representations in the Disentangled

Original: UnshearNet into pose and shear codes respectively.

Original: To do this, we passed the ‘Shear Code’ to theunsheared reconstruction decoder (DC) instead of the ‘Pose Code’.

Original: As expected, this led to a severedegradation in performance with mean-square error (MSE) between the ground truth images C (tap)and unsheared images PC increasing to 0.22, an order of magnitude higher than original of 0.023.

Original: In similar fashion, the SSIM index dropped to 2% when using the Shear Code to reconstruct theunsheared images PC instead of the original 93% when the Pose Code was used.

Original: Likewise, asimilardegradation was observed when the ‘Shear Code’ was replaced by the Pose Code to reconstruct thesheared input S .

Original: The mean-squared error between S and the sheared output PS increased to 0.1, whichwas 50-times the original of 0.002 when both ‘Pose and Shear Codes were used to reconstruct PS .

Original: The

Original: SSIM index showed a similar trend with the similarity dropping from 99 .

Original: 5% to only 11%.

Original: This showsthat the Shear Code is indeed encoding relevant information required for successful reconstruction ofsheared input S .

Original: These results clearly demonstrate that the Disentangled UnshearNet successfullydisentangles the latent representations as desired.

Original: [Figure]