Madeleine Abernot

Sylvain Gauthier

Théophile Gonos

Aida Todri
email: aida.todri@lirmm.fr

Aida Todri-Sanial

SIFT-ONN: SIFT Feature Detection Algorithm Employing ONNs for Edge Detection

Keywords: O scillatory Neural Networks, Image Edge Detection, Feature Detection, SIFT

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Introduction

Navigation is a complex and pervasive problem that allows autonomous robots to navigate safely in an environment without human interaction. Robot navigation is typically divided into various tasks, such as localization to place the robot in its environment from a reference point, obstacle avoidance to avoid obstacles in real-time, and mapping to create an environment map in real-time, among others [START_REF]Mobile robot navigation and obstacle avoidance techniques: A review[END_REF][START_REF] Desouza | Vision for mobile robot navigation: a survey[END_REF].

In state-of-the-art robot navigation, Simultaneous Localization And Mapping (SLAM) is the most widely applied algorithm [START_REF] Bailey | Simultaneous localization and mapping (slam): part ii[END_REF][START_REF] Durrant-Whyte | Simultaneous localization and mapping: part i[END_REF]. SLAM uses sensor data from the robot to estimate robot's current location. Sensor data are also used to create an environment map around the robot. SLAM can use various types of sensors. For example, some SLAM algorithms use cameras as sensors and use captured images to estimate robot position and environment. Another widely applied solution is to combine feature-based object tracking from images with SLAM algorithm [START_REF] Ali | Sift based monocular slam with multi-clouds features for indoor navigation[END_REF][START_REF] Campos | ORB-SLAM3: An Accurate Open-Source Library for Visual, Visual-Inertial, and Multimap SLAM[END_REF][START_REF] Mur-Artal | ORB-SLAM: A Versatile and Accurate Monocular SLAM System[END_REF]. Featurebased object tracking consists of detecting and describing features from two following image frames and matching the corresponding features to compute transformation between two frames, see Fig. 1. In state-of-the-art, SLAM algorithm is combined with ORB (Oriented FAST and Rotated BRIEF) or SURF (Speeded Up Robust Features) algorithms [START_REF] Campos | ORB-SLAM3: An Accurate Open-Source Library for Visual, Visual-Inertial, and Multimap SLAM[END_REF][START_REF] Cocaud | SURF-Based SLAM Scheme using Octree Occupancy Grid for Autonomous Landing on Asteroids[END_REF][START_REF] Mur-Artal | ORB-SLAM: A Versatile and Accurate Monocular SLAM System[END_REF][START_REF] Rublee | Orb: An efficient alternative to sift or surf[END_REF] because they perform fast feature detection and description algorithms.

Even if ORB gives good results, other feature detection and description algorithms can reach better precision but are too slow to compute for real-time navigation applications. For example, the Scale Invariant Feature Transform algorithm (SIFT) [START_REF] Lowe | Distinctive Image Features from Scale-Invariant Keypoints[END_REF][START_REF] Zhou | Object tracking using sift features and mean shift[END_REF] is one of the best-reported feature detection and description algorithms in terms of precision but has large computation latency. In this work, we explore a possible solution to speed up SIFT algorithm while maintaining reasonable precision compared to other algorithms. We choose to investigate SIFT as it is often used as a baseline in various feature detection algorithms. However, our proposed solution is general enough and applicable to other feature detection and description algorithms, such as SURF or others.

We propose and explore massive parallelism of oscillatory neural networks [START_REF] Csaba | Coupled oscillators for computing: A review and perspective[END_REF][START_REF] Endo | Neural network using oscillators[END_REF][START_REF] Nikonov | Coupled-Oscillator Associative Memory Array Operation for Pattern Recognition[END_REF][START_REF] Shukla | Ultra low power coupled oscillator arrays for computer vision applications[END_REF] to reduce the latency of SIFT algorithm. The first stage in SIFT algorithm is the computation of a Difference of Gaussian (DoG), in wich the output resembles an image edge detection algorithm. We propose to use ONNs to perform image edge detection [START_REF] Abernot | Oscillatory Neural Network as Hetero-Associative Memory for Image Edge Detection[END_REF][START_REF] Abernot | Two-Layer Oscillatory Neural Networks for Image Edge Detection: Study of Bidirectional and Feedforward Architectures[END_REF] to replace the first SIFT DoG stage.

The main contributions of the paper can be summarized as i) the development of the hybrid SIFT-ONN algorithm by introducing ONNs for image edge detection at the first stage of the SIFT algorithm, and ii) benchmarking and evaluation of the hybrid SIFT-ONN solution compared to stateof-the-art feature detection and description algorithms in terms of precision and latency.

The paper is organized as follows. First, Section 2 gives an overview of SIFT feature detection and description algorithms. Then, Section 3 presents the ONN computing paradigm and its application to image edge detection. Next, in Section 4, we describe our hybrid SIFT-ONN algorithm by replacing first-stage SIFT DoG with ONN-based image edge detection. Also, in Section 4 we describe the methods to evaluate SIFT-ONN with state-of-the-art algorithms. Section 5 presents the results and benchmarking of the SIFT-ONN. And finally, Section 6 discusses the advantages, limitations, and prospective improvements and future work on SIFT-ONN.

2 Feature detection and description with SIFT Feature detection and description algorithms are used in various applications, such as navigation with SLAM. Here, we present state-of-the-art approaches on feature detection and description algo-rithms for navigation tasks. Also, we describe the different computation stages in the SIFT algorithm.

State-of-the-art

Over the last twenty years, various feature detection and description algorithms have been proposed. Most feature detection algorithms are based on edge or corner detection algorithms. Mainly, their differences are in the mathematical approaches to detect features or edges and corners, and in the methods to define the descriptors of the features used to match them. Important parameters are scale and rotation invariance, which are necessary to detect and describe features for matching two images with different points of view. SIFT is one of the first feature detection and description algorithms introduced with scale and rotation invariance [START_REF] Lowe | Distinctive Image Features from Scale-Invariant Keypoints[END_REF], which obtains high precision while using large computing resources but also results in long computation time. Since SIFT, other solutions have been proposed to reduce computation latency depending on the target applications [START_REF] Alcantarilla | Computer Vision -ECCV 2012[END_REF][START_REF] Bay | SURF: Speeded Up Robust Features[END_REF][START_REF] Leutenegger | Brisk: Binary robust invariant scalable keypoints[END_REF][START_REF] Rublee | Orb: An efficient alternative to sift or surf[END_REF]. For example, in mobile robotics, SIFT has been successively replaced by SURF [START_REF] Bay | SURF: Speeded Up Robust Features[END_REF] and ORB [START_REF] Rublee | Orb: An efficient alternative to sift or surf[END_REF], which are faster, therefore, more suitable for realtime constrained applications. In this work, we investigate applying ONN image edge detection to replace SIFT DoG in order to reduce SIFT computation latency.

Scale Invariant Feature Transform (SIFT) Algorithm

SIFT stands for Scale Invariant Feature Transform [START_REF] Lowe | Distinctive Image Features from Scale-Invariant Keypoints[END_REF]. SIFT is a feature detection and description algorithm, which is scale and rotation invariant. It aims to correctly detect and describe features to be able to match them between two images, even if they are rotated, with different sizes and scales.

The SIFT feature detection and description algorithm can be divided into four main stages, as shown in Fig. 1. The first stage detects extrema in various scale spaces. More precisely, it uses DoG to detect edges in images smoothed by gaussian blur filters with different smoothing scales. For each pixel at position (x, y) in the image, it computes:

D(x, y, σ) = L(x, y, kσ) -L(x, y, σ) (1)
G(x, y, σ) = 1 2πσ 2 e -(x 2 +y 2 )/2σ 2 (3) (2)
where D is the DoG output, L is the output image after the Gaussian blur is applied, G is the Gaussian blur, and σ is the smoothing scale, see Fig. 2. Then, extrema are extracted from the DoG outputs. For each octave, each pixel of a scale space is compared with its 8 neighboring pixels from the same scale space, and with its 9 neighboring pixels from lower and upper scale spaces. Extrema are pixels with the highest or smallest values compared to all 26 neighbors, see Fig. 2.

The second stage of SIFT is to select key points from the extracted extrema. Low extrema are filtered to obtain only the strong key points that are easily reproducible in different images. Extrema on edges are also filtered because edges are sensitive to noise and DoG is highly sensitive to edges. After localizing the key points, their orientation is computed. SIFT computes for each key point the magnitude and orientation on a 16x16 window. Then, it groups pixels in 4x4 windows to create orientation histograms. In this case, orientation and magnitude in each 4x4 window are combined. Then, the main orientation from each 4x4 histogram is extracted. Fig. 3 shows the feature orientation process with histograms and orientation definitions. The final stage creates the descriptors, which are vectors containing main orientations with magnitude around each key point, making descriptors scale and rotation invariant.

Once SIFT is applied to two images, descriptors from both images are matched. Matched descrip- tors are used to determine the transformation between the two images. For example, in the case of two following images from a moving robot, the transformation can be associated with the movement of the robot. Note, it is possible to filter the number of matches used to compute the transformation to impact the obtained transformation value.

ONN for image edge detection

ONN is a promising neuromorphic computing paradigm for edge artificial intelligence applications due to its energy efficient and massive parallel computations [START_REF] Delacour | Energy-Performance Assessment of Oscillatory Neural Networks based on VO2 Devices for Future Edge AI Computing[END_REF].

ONN computing paradigm

ONN is a brain-inspired paradigm where the computations are performed on coupled oscillators [START_REF] Csaba | Coupled oscillators for computing: A review and perspective[END_REF]. In ONNs, each neuron is an oscillator coupled with synapses, which can be implemented either in analog or digital. ONNs encode information in the phase relationship among oscillators. For example, with binary information, a logic 0 is represented with an oscillator phase of 0 o , and a logic 1 is represented with an oscillator phase of 180 o . Phasebased computing allows to lower voltage amplitude, thus reducing power consumption. ONNs use the dynamics of coupled oscillators for inference. At first, oscillator phases are initialized from input information. Then, phases evolve in a parallel fashion depending on the coupling strength among oscillators. Finally, oscillators stabilize and their phases are read to construct the output information. Overall, both low power and parallel computations make ONN attractive for edge computing.

In literature, ONNs are typically designed as a fully-connected recurrent architecture, and trained with unsupervised learning rules, like Hebbian, to solve pattern recognition or auto-associative memory tasks, as in Hopfield neural networks [START_REF] Hopfield | Neural networks and physical systems with emergent collective computational abilities[END_REF][START_REF] Morris | The Organization of Behavior[END_REF]. Recently, authors in [START_REF] Abernot | Oscillatory Neural Network as Hetero-Associative Memory for Image Edge Detection[END_REF][START_REF] Abernot | Two-Layer Oscillatory Neural Networks for Image Edge Detection: Study of Bidirectional and Feedforward Architectures[END_REF], reported on a twolayer ONN architecture with feedforward connectivity that can efficiently solve image edge detection tasks. Fig. 4.a) illustrates the ONN computing paradigm with a two-layer feedforward architecture configured for classification.

In this work, we utilize the feedforward digital ONN implemented on FPGA as in [START_REF] Abernot | Digital implementation of oscillatory neural network for image recognition applications[END_REF][START_REF] Abernot | Oscillatory Neural Network as Hetero-Associative Memory for Image Edge Detection[END_REF][START_REF] Abernot | Two-Layer Oscillatory Neural Networks for Image Edge Detection: Study of Bidirectional and Feedforward Architectures[END_REF], see Fig.

ONN edge detection

Here, we investigate in incorporating the feedforward ONN architecture configured for image edge detection to be part of the SIFT algorithm. In literature, image edge detection uses convolutional filters, typically 3x3, 5x5, or 7x7, to scan an image and detect edges. Sobel [START_REF] Sobel | A 3×3 isotropic gradient operator for image processing[END_REF] and Canny [START_REF] Canny | A Computational Approach to Edge Detection[END_REF] are the two main convolutional-based edge detection algorithms.

ONNs for image edge detection are introduced in [4] using a two-layer ONN connected with bidirectional connections that perform hetero-associative memory tasks. In [START_REF] Abernot | Oscillatory Neural Network as Hetero-Associative Memory for Image Edge Detection[END_REF], authors use Sobel convolutional filters as training patterns to compute synaptic couplings between the two ONN layers. However, such architecture had some missing edges, thus in [START_REF] Abernot | Two-Layer Oscillatory Neural Networks for Image Edge Detection: Study of Bidirectional and Feedforward Architectures[END_REF], authors proposed a customization of the coupling weights to improve the precision of the two-layer bidirectional architecture. Nevertheless, the two-layer bidirectional ONN architecture has important latency limitations, and uses a large amount of digital resources, limiting the number of possible ONNs that can be implemented in parallel in order to reduce latency. Thus, in [START_REF] Abernot | Two-Layer Oscillatory Neural Networks for Image Edge Detection: Study of Bidirectional and Feedforward Architectures[END_REF], authors introduced instead an architecture with a two-layer feedforward ONN. Authors reported on feedforward ONN for image edge detection with various sizes (3x3, 5x5, and 7x7) to scan the image, see Fig. 5. Using a larger size ONN can increase the stride and help reduce the image scanning latency. In [START_REF] Abernot | Two-Layer Oscillatory Neural Networks for Image Edge Detection: Study of Bidirectional and Feedforward Architectures[END_REF], it was shown that feedforward ONN for image edge detection has similar precision as the state-of-the-art Sobel algorithm, and it can achieve better latency by using multiple ONNs in parallel. Table 1 highlights the main characteristics of the feedforward digital ONN. Note, the ONN configured for image edge detection from [START_REF] Abernot | Two-Layer Oscillatory Neural Networks for Image Edge Detection: Study of Bidirectional and Feedforward Architectures[END_REF] only outputs binary phase information 0 o , 180 o .

In the SIFT algorithm, the DoG computation can be approximated to an edge detection computation. Thus, in this work, we aim to replace the SIFT DoG stage with 3x3, 5x5, or 7x7 feedforward ONN for image edge detection-creating a hybrid

SIFT-ONN adaptation

Here, we replace the DoG with the feedforward ONN for image edge detection.

In the first stage of SIFT, a first pyramid is generated from the input image by resizing it to create various octaves. The first octave is composed of the input image upsampled by two, and the following octaves are generated by subsampling by two of their previous octave until the size is too small to make a Euclidean division by two. Then, a second pyramid is created by applying various gaussian blurs on the image from each octave to create different scales of the same image, see Fig. 2. Next, the DoG outputs are computed for each octave between neighboured gaussian blurs to obtain images with highlighted edges. In this work, the SIFT-ONN keeps the generation of the first pyramid, creating octaves by subsampling the input image. Then, the gaussian blurs are replaced with image binarization with various black-and-white thresholds. Next, the ONN for edge detection is applied to each generated black-and-white image to obtain images with highlighted edges. Finally, the ONN edge detection output images replace the SIFT DoG stage output for the rest of the SIFT algorithm, see Fig. 6. Fig. 7 shows time estimations to scan all generated images from a 512x512 input image with parallel feedforward ONNs. The number of parallel ONNs is defined from the maximum resource utilization of the Zybo Z7 board, which is equipped with a Xilinx Series-7 FPGA. Fig. 7 highlights that using a stride of the size of the filter really improves latency. In [START_REF] Abernot | Two-Layer Oscillatory Neural Networks for Image Edge Detection: Study of Bidirectional and Feedforward Architectures[END_REF], authors assigned the ONN output to the full selected window to avoid discontinuities. However, in SIFT-ONN, tests showed the precision is higher if only the central pixel is assigned, even though it induces discontinuities. Thus, for the rest of the paper, the ONN output is assigned to the central pixel of the scanning window. For example, for a 3x3 ONN filter, the stride is equal to 3, and the ONN output is assigned to the central pixel of the 3x3 window.

Validation and evaluation methods

The feedforward ONN is validated and evaluated for image edge detection in [START_REF] Abernot | Two-Layer Oscillatory Neural Networks for Image Edge Detection: Study of Bidirectional and Feedforward Architectures[END_REF] using the digital design of Fig. 4.b) implemented on FPGA. In this work, the feedforward ONN configured for image edge detection is first emulated in python with a Hopfield-based feedforward network. It allows using the built-in functions of SIFT algorithm from Python libraries [START_REF]A clean and concise python implementation of sift (scale-invariant feature transform[END_REF] combined with the ONN image edge detection. Also, it allows comparing precision and latency with other state-of-the-art feature detection and description algorithms available in Python libraries. However, in order to have a better latency assessment of the SIFT-ONN, we estimate the latency of the digital feedforward ONN on various image sizes.

Dataset

This work uses a custom dataset generated from 36 standard 256x256 and 512x512 gray scale images. Each image is resized and normalized to a 512x512 size and becomes a base image. Then, 5 sub-images are generated by applying rotation, perspective and size transformations from each 512x512 base image. Thus, the full dataset contains 36 base images, and 180 transformed images.

Hopfield-based emulator in Python for precision evaluation

SIFT-ONN is validated in python using a Hopfieldbased emulator of the digital feedforward ONN configured for image edge detection combined with built-in SIFT Python functions [START_REF]A clean and concise python implementation of sift (scale-invariant feature transform[END_REF]. Precision is obtained using images from the dataset applied to image relocation application. In feature detection and description algorithms, precision is evaluated by checking repeatability. An algorithm is repeatable if features can be correctly detected in images before and after transformation. In this work, to assess SIFT-ONN repeatability, the goal is to retrieve the position of parts of an image, the sub-images from dataset, in the original image, the corresponding base image from dataset. To do so, feature detectors and descriptors are first generated from all base and sub-images using the SIFT-ONN feature detection and description algorithm and matched between the sub-images and the corresponding base image. Matching is performed using brute force approach. From matching between one base image and one sub-image, a transformation is computed, and the corresponding position of the sub-image in the base image is defined. The obtained position is then compared with the real position of the sub-image, obtained during its generation, using the Jaccard Similarity Coefficient (JSC) [START_REF] Chung | Jaccard/Tanimoto similarity test and estimation methods for biological presence-absence data[END_REF]. JSC computes the ratio of intersection over union pixels between the real sub-image position, and the computed sub-image position.

JSC = Intersection U nion (4)
The JSC final score is computed performing a mean of the JSC scores of all sub-images. Moreover, we use the same method with other stateof-the-art feature detection and description algorithms to have a consistent benchmark of the SIFT-ONN solution.

Digital ONN for latency assessment

After assessing the precision and repeatability of the SIFT-ONN, it is necessary to evaluate its computation time. Using parallelism for the ONN edge detection in Python is difficult, so for the Python tests with a Hopfield-based emulator, we consider sequential treatment, which makes the computation time really high, around hundreds of seconds. However, considering the digital feedforward ONN implemented on FPGA, it is possible to implement multiple ONNs in parallel to improve latency. Thus, to evaluate and compare the latency of SIFT-ONN with state-of-the-art algorithms, we use estimations of digital ONN latency to scan images using parallel ONNs combined with a computation time of later steps of SIFT-ONN from SIFT Python libraries. The latency of SIFT Python libraries is estimated based on the GeForce GTX 1050 Mobile GPU hardware.

Results

Here, we present results obtained with the SIFT-ONN solution in terms of precision, latency, and compared them with well-known feature detection and description algorithms. SIFT-ONN is compared with SURF, ORB, BRISK, SIFT, and KAZE as they are state-of-the-art feature detection and description algorithms.

Precision

Fig. 8 highlights the JSC mean score obtained for each tested algorithm depending on the percentage of matches used for transformation. Note, SIFT-ONN is tested with the three ONN filter sizes: 3x3, 5x5, and 7x7, and in each case, the stride of image scanning is equal to the filter size. For example, a stride of 3 for the 3x3 filter. Also note that when scanning with a stride of the size of the filter, the ONN output is applied only to the central pixel of the 3x3 window scanned. Table 2 presents the real computation times obtained with the sequential process of a 3x3 Hopfield emulator, the estimated computation time obtained with digital 3x3 ONN implemented on FPGA and precision for scanning strides equal to 1 and 3 with no filtered matches. It highlights that scanning with a stride of the size of the filter does not diminish the precision score, it even increases it. However, it really decreases the real latency to test on Python, as well as the estimated latency. Thus, we do not consider small strides due to the long computation time. Fig. 8 shows that SIFT-ONN reduces SIFT precision score by a factor larger than two. SIFT-ONN precision score is also lower than BRISK, SURF, and KAZE results, but similar to ORB for most of the cases. SIFT-ONN with a 3x3 filter gives the best precision score compared with larger ONN filter sizes.

Latency

Discussion

This work presents an adaptation of SIFT feature detection and description algorithm by using a hybrid SIFT-ONN solution. In the SIFT-ONN, a feedforward ONN for image edge detection [START_REF] Abernot | Two-Layer Oscillatory Neural Networks for Image Edge Detection: Study of Bidirectional and Feedforward Architectures[END_REF] replaces the original SIFT DoG stage. The aim of SIFT-ONN is to reduce SIFT computation time, while keeping high precision to allow feature detection and description on edge devices.

First, it is important to highlight that SIFT-ONN adaptation does not require important changes. Only the SIFT scale generation and DoG stages are replaced with the ONN image edge detection. However, the following SIFT stages do not require any change. Yet, the results show the SIFT-ONN solution induces a drastic reduction of precision in comparison with SIFT, by a factor of 2. This decrease is mainly due to the binary ONN edge detection output. The DoG from SIFT algorithm outputs gray-scale images with various edge strengths such as strong or weak edges, while the ONN edge detection outputs black-and-white images with binary edge information. Thus, this binary output can have a consequence in the extrema definition. Each edge can become a maximum, and each background can become a minimum, depending on the position. However, in principle, ONN can stabilize to non-binary phases among 0 o -360 o range. Thus, a solution to improve ONN-SIFT precision is to investigate how to perform ONN image edge detection with non-binary ONN outputs. Additionally, this work does not compare SIFT-ONN with SIFT adapted with other image edge detection algorithms, such as state-of-the-art Sobel [START_REF] Sobel | A 3×3 isotropic gradient operator for image processing[END_REF] or Canny [START_REF] Canny | A Computational Approach to Edge Detection[END_REF]. Both algorithms generate gray-scale images with various edge significance, thus it can help assess if a gray-scale ONN edge detection could solve feature detection and description with higher precision.

Furthermore, during tests, some divergences in the precision results were observed between two python simulations with equal parameters. Thus, we believe the generated dataset may not be large enough to clearly assess the precision of the SIFT-ONN algorithm and further tests are necessary. However, due to the large computation time, it was not possible to enlarge the dataset. Additionally, precision is tested on the image relocation application. However, it is also important to test feature detection and description algorithms on other applications, like image occlusion. Thus, additional tests on a larger dataset and on additional applications are also necessary to have a better assessment of the SIFT-ONN precision.

Still, SIFT-ONN is close to ORB performances both in terms of precision and estimated latency. ORB is currently a standard to perform feature detection and description on embedded devices due to its fast computation time, even though precision is lower than other state-of-the-art algorithms. Thus, the SIFT-ONN can become an alternative to ORB for feature detection and description, for example, in robotic applications. Furthermore, ONN shows promising low-power computation properties [START_REF] Delacour | Energy-Performance Assessment of Oscillatory Neural Networks based on VO2 Devices for Future Edge AI Computing[END_REF], which can be advantageous for edge computing in robotic applications.

Finally, this work aims to present, validate, and evaluate the SIFT-ONN solution, but up to now, there is no hardware demonstrator implemented. In literature, it is reported various FPGA implementations of SIFT [START_REF] Bonato | A parallel hardware architecture for scale and rotation invariant feature detection[END_REF][START_REF] Peng | Fpga-based parallel hardware architecture for sift algorithm[END_REF], so future work is to develop a real-time full FPGA implementation of the SIFT-ONN algorithm.

Conclusion

This work explores the SIFT-ONN solution to accelerate the SIFT feature detection and description algorithm to make it suitable for embedded applications with important latency constraints, such as in robotic navigation. The SIFT-ONN solution replaces the SIFT Difference of Gaussian stage with an image edge detection algorithm based on the promising Oscillatory Neural Network (ONN) neuromorphic computing paradigm. ONNs are currently being explored for their fast and low-power computation, which can be suitable for embedded feature detection and description applications. SIFT-ONN is an adaptation of SIFT which does not require major changes. The SIFT-ONN induces a diminution of the SIFT precision by a factor of two, however, latency estimations based on a digital implementation of the ONN image edge detection algorithm are promising, reducing latency also by a factor of two. Thus, SIFT-ONN performances are comparable with the ORB algorithm, which is the state-of-the-art feature detection and description algorithm for robotic navigation applications and other applications with fast timing requirements. Finally, this work is the first investigation to use the ONN computing paradigm as a hardware accelerator for image processing algorithms, and results are encouraging to explore further image processing tasks.

Figure 1 :

 1 Figure 1: Robot movement computation based on SIFT feature detection and description algorithm and matching.

Figure 2 :

 2 Figure 2: Detection of scale space extrema based on Difference of Gaussians.

Figure 3 :

 3 Figure 3: Feature orientation.

Figure 4 :

 4 Figure 4: a) Feedforward ONN architecture for classification. b) Digital feedforward ONN implementation on FPGA.

  4.b). Each oscillator is a 16-stage phasecontrolled oscillator allowing phases between 0 o and 360 o with phase precision of 22.5 o . Oscillators from the output layer also include a phase calculator, which integrates post-synaptic phases from the input layer. Synapses are 5-bits signed registers allowing integer weights between -15 and 15.

Figure 5 :

 5 Figure 5: Feedforward ONN configured for image edge detection applied to a black and white image.

Figure 7 :

 7 Figure 7: ONN edge detection latency estimation for SIFT-ONN 512x512 image process.

Figure 8 :

 8 Figure 8: Precision scores of feature extraction algorithms compared with SIFT-ONN solution.

Figure 9 :

 9 Figure 9: Latency of feature extraction algorithms compared with SIFT-ONN solution.

Fig. 9

 9 Fig.9shows latency estimations of ONN-SIFT for various ONN filter sizes, considering the digital ONN design, compared with the latency of stateof-the-art algorithms computed in Python based on the GeForce GTX 1050 Mobile GPU hardware. It shows the ONN filter size does not affect much the global SIFT-ONN latency. SIFT-ONN improves latency from the original SIFT algorithm and reduces it approximately by a factor of two. Fig.10combines both precision score and latency results to highlight SIFT-ONN moves the SIFT algorithm in the same precision, and latency ranges as ORB, with a lower precision but a faster computation time.

Figure 10 :

 10 Figure 10: Combination of precision score and latency of SIFT-ONN compared with state-of-the-art feature detection and description algorithms.

Table 1 :

 1 Characteristics of edge detection feedforward ONN from[START_REF] Abernot | Two-Layer Oscillatory Neural Networks for Image Edge Detection: Study of Bidirectional and Feedforward Architectures[END_REF].

	ONN	3x3	5x5	7x7
	Latency	1.15 µs 1.15 µs 1.15 µs
	LUTs	211	302	457
	Flip-Flops	277	437	597

Figure 6: SIFT-ONN algorithm process. SIFT-ONN algorithm.

Table 2 :

 2 ONN-SIFT real computation time based on python processing, estimated computation time based on digital ONN estimations, and score for a 3x3 ONN filter size for two scanning strides and no filtered matches.

	Stride	1	3
	Real comp. time (s)	3712	563
	Est. comp. time (s) 0.0878 0.0632
	JSC score	0.16	0.28

Acknowledgement

We thank T. Gil (LIRMM -CNRS), M. Jimenez, J. Nunez, and M. J. Avedillo (IMSE -CSIC) for fruitful exchanges and constructive suggestions on this research work.

* This work was supported by the European Union's Horizon 2020 research and innovation program, EU H2020 NEU-RONN project under grant n. 871501 (www.neuronn.eu).


Jesús González-Cobos

Mathieu S Prévot

Philippe Vernoux
email: philippe.vernoux@ircelyon.univ-lyon1.fr

Electrolysis of lignin for production of chemicals and hydrogen

Keywords: Lignin, Electrolysis, Hydrogen, Oxidation, Kinetics

Lignin electrolysis offers the possibility of cogenerating valuable aromatic compounds and green H2 under mild conditions and with a lower energy cost than traditional water electrolysis. In recent years, significant progress has been accomplished towards this objective through the development of active electrocatalysts and the engineering of cell configuration. This short review gives an overview of the anode materials and cells investigated in acidic and alkaline conditions, below and above 100°C and summarizes the main bottlenecks which remain to be addressed. Low-temperature electrolysers could be integrated in biorefineries to convert lignin into higher-value industrial chemicals with co-generation of hydrogen.

Introduction

Green H2, generated with renewable energies without CO2 emissions, will play a key role in the energy transition [1,2]. It is mainly produced by water electrolysis either at low temperature (< 100ºC) in alkaline water electrolyzers (AWE) or proton/anion-exchange membrane (PEM/AEM) electrolyzers, or at high temperature (500-1000ºC) in solid oxide electrolyzers (SOE) [2,[START_REF] El-Shafie | Hydrogen Production Technologies Overview[END_REF], all of them producing H2 and O2 at their respective cathodes and anodes. However, the oxygen evolution reaction (OER) suffers from thermodynamic and kinetic limitations that must be overcome to make this technology more competitive. One possible solution is to replace the OER by a less-energy intensive reaction, like the oxidation of bio-sourced alcohols [START_REF] Liu | Recent advances in paired electrolysis of biomass-derived compounds toward cogeneration of value-added chemicals and fuels[END_REF][START_REF] Simões | Electrochemical valorisation of glycerol[END_REF][START_REF] Tuomi | Hydrogen production by methanol-water solution electrolysis with an alkaline membrane cell[END_REF][START_REF] Caravaca | Electrochemical reforming of ethanol-water solutions for pure H2 production in a PEM electrolysis cell[END_REF][START_REF] Caravaca | From biomass to pure hydrogen: Electrochemical reforming of bio-ethanol in a PEM electrolyser[END_REF][START_REF] Marshall | Production of hydrogen by the electrochemical reforming of glycerol-water solutions in a PEM electrolysis cell[END_REF][START_REF] Linares | Chapter 4: Electrochemical Reforming of Alcohols, RSC Energy and Environment Series[END_REF][START_REF] Coutanceau | Electrochemical conversion of alcohols for hydrogen production: a short overview[END_REF], but the use of these substrates directly competes with food resources (cropland). Alternatively, this review describes recent advances of the electrolysis of lignin, a highly-abundant natural and chemically-rich polyphenolic polymer (Figure 1a) representing up to 40 wt.% of woody wastes, but currently mostly treated as worthless byproduct: for instance, Kraft lignin, coming from the residues of chemical pulping in paper production, is usually simply incinerated to produce heat [START_REF] Du | Low-Energy Catalytic Electrolysis for Simultaneous Hydrogen Evolution and Lignin Depolymerization[END_REF][START_REF] Liu | Identifying and creating pathways to improve biological lignin valorization[END_REF][START_REF] Wang | From lignin to valuable products-strategies, challenges, and prospects[END_REF]. Indeed, at the moment, only a small part of lignin waste is valorized into valuable chemicals (e.g. vanillin, vanillic acid, benzene, toluene, xylenes) by emerging processes such as pyrolysis, gasification, or catalytic oxidation and reduction [START_REF] Wang | From lignin to valuable products-strategies, challenges, and prospects[END_REF][START_REF] Cao | Lignin valorization for the production of renewable chemicals: state-of-the-art review and future prospects[END_REF][START_REF] Zakzeski | Catalytic lignin valorization process for the production of aromatic chemicals and hydrogen[END_REF][START_REF] Kumar | Lignin Biorefinery: New Horizons in Catalytic Hydrodeoxygenation for the Production of Chemicals[END_REF].

Lignin electrolysis (Figure 1b) combines lignin selective electrooxidation at the anode with green H2 production at the cathode [START_REF] Caravaca | Towards a sustainable technology for H2 production: Direct lignin electrolysis in a continuous-flow Polymer Electrolyte Membrane reactor[END_REF][START_REF] Stiefel | Controlled depolymerization of lignin in an electrochemical membrane reactor[END_REF][START_REF] Naderinasrabadi | The authors tested a NiCo-TiO 2 catalyst in an AEM cell for the electrolysis of a biorefinery lignin at room temperature, by performing the longest-term electrolysis tests (24 h) reported in the field and quantified[END_REF][START_REF] Beliaeva | New insights into lignin electrolysis on nickel-based electrocatalysts: Electrochemical performances before and after oxygen evolution[END_REF][START_REF] Lalvani | Lignin-Augmented Water Electrolysis[END_REF][START_REF] Lalvani | Hydrogen production from lignin-water solution by electrolysis[END_REF][START_REF] Ghatak | Electrolysis of black liquor for hydrogen production: Some initial findings[END_REF][START_REF] Ghatak | Electrode processes in black liquor electrolysis and their significance for hydrogen production[END_REF][START_REF] Movil | Non-precious metal nanoparticle electrocatalysts for electrochemical modification of lignin for low-energy and cost-effective production of hydrogen[END_REF][START_REF] Hibino | Hydrogen Production by Direct Lignin Electrolysis at Intermediate Temperatures[END_REF][START_REF] Bateni | explored the use of PbO2 nanoparticles impregnated on multi-walled carbon nanotubes as anode in an AEM cell for lignin electrolysis and found highly pure hydrogen production at 30 mA cm -This is also the only study with anodic product quantification using a direct lignin electrolysis cell at low temperature[END_REF][29], operating under mild and safe conditions (low temperature and atmospheric pressure). Among the pioneering works exploring the direct and indirect use of lignin in fuel cell technology, one can find examples of direct lignin fuel cells operating at low (<100°C) [START_REF] Liu | Efficient direct lignin fuel cells enabled by hierarchical nickel-iron phosphide nanosheets as an anode catalyst[END_REF] and high (560°C) [START_REF] Lima | Direct lignin fuel cell for power generation[END_REF] temperature, both operating at 24 mW.cm -2 . Moreover, indirect lignin fuel cell mediated by a polyoxometalate was reported to deliver 5 mW.cm -2 at 90°C) [START_REF] Zhao | Efficient Conversion of Lignin to Electricity Using a Novel Direct Biomass Fuel Cell Mediated by Polyoxometalates at Low Temperatures[END_REF]. Finally, advanced novel concepts involving lignin electrochemistry are emerging, such as combining lignin electrooxidation with the hydrogenation of H2-lean liquid organic hydrogen carriers (LOHC) [START_REF] Centi | Advanced (photo)electrocatalytic approaches to substitute the use of fossil fuels in chemical production[END_REF]. In the field of lignin electrolysis, recent research efforts have been classified according to their operation temperature: below 100°C in PEM/AEM-like electrolysers or at higher temperatures, using innovative materials and cell designs. It should be noted that, from the anodic products point of view, the high variability of the lignin source composition and the wide variety of potential oxidation/depolymerization/re-polymerization reactions, lead to very complex reactants/products distributions that would be the subject of another specific review article.

Current trends in direct lignin electrolysis for hydrogen production i) Low temperature (< 100°C) lignin electrooxidation

Several studies describe the electro-oxidation of pure lignin or black liquor (lignocellulosic effluent with a lignin concentration of about 40%) on noble metal anodes [START_REF] Caravaca | Towards a sustainable technology for H2 production: Direct lignin electrolysis in a continuous-flow Polymer Electrolyte Membrane reactor[END_REF][START_REF] Lalvani | Lignin-Augmented Water Electrolysis[END_REF][START_REF] Lalvani | Hydrogen production from lignin-water solution by electrolysis[END_REF][START_REF] Ghatak | Electrode processes in black liquor electrolysis and their significance for hydrogen production[END_REF][START_REF] Beliaeva | Towards Understanding Lignin Electrolysis: Electro-Oxidation of a β-O-4 Linkage Model on PtRu Electrodes[END_REF] in standard batch 3electrode cells using liquid electrolytes at low temperature (up to 90 °C) and at lower potentials than OER. In general, electrocatalytic performances were found to increase with lignin concentration, temperature and applied voltage. Kraft lignin electrooxidation has been performed in a flow-through AEM electrolyser equipped with a commercial bimetallic Pt1Ru1 anode supported on carbon cloth [START_REF] Caravaca | Towards a sustainable technology for H2 production: Direct lignin electrolysis in a continuous-flow Polymer Electrolyte Membrane reactor[END_REF].

with an onset voltage of ~0.45 V at 80ºC, which is much lower than that of water electrolysis (Figure 1c). However, the obtained current densities were below 7 mA cm -2 at 1 V, highlighting the kinetic limitations of the process, attributed to the difficult C-C cleavage required for lignin depolymerization and the strong deactivation of the anode by adsorbed reaction intermediates and products. These limitations were later confirmed by the study of the electrolysis of 2-Phenoxyethanol, a model molecule exhibiting the β-O-4 linkage [START_REF] Liu | Efficient direct lignin fuel cells enabled by hierarchical nickel-iron phosphide nanosheets as an anode catalyst[END_REF] representing 50-65% of lignin interunit linkages [START_REF] Beliaeva | Towards Understanding Lignin Electrolysis: Electro-Oxidation of a β-O-4 Linkage Model on PtRu Electrodes[END_REF]. (in red), guaiacyl alcohol (in blue) and p-coumaryl alcohol (in green) units. Reprinted with permission from Ref. [START_REF] Karunarathna | Valorization of Lignin as a Sustainable Component of Structural Materials and Composites: Advances from 2011 to 2019[END_REF]. b) Scheme of a lignin electrolyser. c) Linear sweep voltammetry measured in an AEM electrolyser from 0 to 0.9 V at 80°C; scan rate: 0.5 mV s -1 , in an AEM lignin electrolyser with PtRu/C anode and Fumapem FAA-3 membrane; anolyte: 1 M NaOH (black) or 10 g L -1 lignin in 1 M NaOH (red). The non-zero current for water electrolysis as observed in many studies can be due i) the oxidation of the electrode materials, ii) the formation of oxygen-or hydroxyl-surface species from water dissociation (below OER potential), or iii) the charging current. Reprinted with permission from Ref. [START_REF] Caravaca | Towards a sustainable technology for H2 production: Direct lignin electrolysis in a continuous-flow Polymer Electrolyte Membrane reactor[END_REF].

Non-noble anode materials such as Ni-based (pure or alloyed with Sn or Co) [START_REF] Naderinasrabadi | The authors tested a NiCo-TiO 2 catalyst in an AEM cell for the electrolysis of a biorefinery lignin at room temperature, by performing the longest-term electrolysis tests (24 h) reported in the field and quantified[END_REF][START_REF] Beliaeva | New insights into lignin electrolysis on nickel-based electrocatalysts: Electrochemical performances before and after oxygen evolution[END_REF][START_REF] Bateni | explored the use of PbO2 nanoparticles impregnated on multi-walled carbon nanotubes as anode in an AEM cell for lignin electrolysis and found highly pure hydrogen production at 30 mA cm -This is also the only study with anodic product quantification using a direct lignin electrolysis cell at low temperature[END_REF]29,[START_REF] Ghahremani | Electrochemical oxidation of lignin for the production of valueadded chemicals on Ni-Co bimetallic electrocatalysts[END_REF] and PbO2 [28] [38] were also investigated in alkaline media, although lower current densities were obtained, vs. PtRu, at low potentials (e.g., below 2 mA cm -2 at 1 V on Ni(OH)2 [START_REF] Beliaeva | New insights into lignin electrolysis on nickel-based electrocatalysts: Electrochemical performances before and after oxygen evolution[END_REF]). According to Table 1, best reported current densities reach 30 mA cm -2 , a value that remain far below the typical specifications of water AEM electrolyzers (from 0.2 to 2 A cm -2 at 1.4 -2.0 V) [2,3], tentatively attributed to the limited a)

Lignin electrolysis c) b)

lignin depolymerization kinetics and to anode deactivation phenomena. The most notable results, in terms of H2 production, have been obtained with the NiCo-TiO2 electrode proposed by Naderi Nasrabadi et al., with 2.3 mL min -1 measured after 24 hours polarization at 1.7 V, corresponding to an energy consumption of 4.1 kWh per Nm 3 H2 [START_REF] Naderinasrabadi | The authors tested a NiCo-TiO 2 catalyst in an AEM cell for the electrolysis of a biorefinery lignin at room temperature, by performing the longest-term electrolysis tests (24 h) reported in the field and quantified[END_REF]. However, at this high potential, OER was significantly more favoured than lignin electrooxidation and any increase of lignin concentration was detrimental due to the blockage of the electrode pores and its catalytic sites. Moreover, Beliaeva et al. operated an AEM cell with a Ni-based anode at 80°C at a voltage as low as 1.1 V [START_REF] Beliaeva | New insights into lignin electrolysis on nickel-based electrocatalysts: Electrochemical performances before and after oxygen evolution[END_REF] and decreased the energy consumption rate to 2.6 kWh per Nm -3 H2, much lower than that required in water electrolysers (e.g., 4.3 kWh Nm -3 H2 at 1.8 V). Interestingly, even lower energy consumption can be achieved by adding a redox mediator in the electrolyte. This mediator chemically oxidizes the organic substrate in the anolyte and is subsequently electrochemically reoxidized (regenerated) on the anode. Many redox mediators have been reported in the literature for the electrooxidation of lignin and model phenolic compounds, as recently reviewed by Du et al. [START_REF] Du | Electrochemical Lignin Conversion[END_REF], such as nitroaromatics [START_REF] Smith | Biomass electrochemistry: Anodic oxidation of an organo-solv lignin in the presence of nitroaromatics[END_REF][START_REF] Pardini | Electroorganic reactions. 38. Mechanism of electrooxidative cleavage of lignin model dimers[END_REF], halides [START_REF] Gao | Selective electrochemical CO bond cleavage of β-O-4 lignin model compounds mediated by iodide ion[END_REF], polyoxometalates (POMs) [START_REF] Du | Low-Energy Catalytic Electrolysis for Simultaneous Hydrogen Evolution and Lignin Depolymerization[END_REF][START_REF] Liu | High efficiency hydrogen evolution from native biomass electrolysis[END_REF] or transition metal ions [START_REF] Du | Low-Energy Catalytic Electrolysis for Simultaneous Hydrogen Evolution and Lignin Depolymerization[END_REF]. For instance, H3PMo12O40 [START_REF] Liu | High efficiency hydrogen evolution from native biomass electrolysis[END_REF] and FeCl3 [START_REF] Du | Low-Energy Catalytic Electrolysis for Simultaneous Hydrogen Evolution and Lignin Depolymerization[END_REF] can oxidize biomass under heating (<100°C) or irradiation (UV) for few hours generating reduced POM and Fe 2+ species which are electrochemically reoxidized in acidic conditions at 100ºC on a noble metal-free anode like a pure graphite felt material. This indirect lignin electrolysis consumes only 0.69 kW h Nm -3 H2 at 0.2 A cm -2 [START_REF] Du | Low-Energy Catalytic Electrolysis for Simultaneous Hydrogen Evolution and Lignin Depolymerization[END_REF].

The electrooxidation of lignin can produce many different valuable aromatics like vanillin, vanillic acid, sinapic acid or acetovanillone [START_REF] Fidio | Electro-oxidative depolymerisation of technical lignin in water using platinum, nickel oxide hydroxide and graphite electrodes[END_REF]. For instance, the group of Staser [29] observed that Ni and Sn-doped Ni-based anodes can generate vanillin, a high-value chemical, in alkaline media, with a maximum production rate of 300 mg kglignin -1 min -1 at 1.4 V at RT while at higher voltages the OER predominates. The promoting effect of cobalt on nickel not only enhances the current densities and lowers the onset oxidation potential, as already observed for other electrooxidation reactions [START_REF] Brousse | To Be or Not To Be Pseudocapacitive?[END_REF][START_REF] Cui | Promoting Effect of Co in NimCon (m + n = 4) Bimetallic Electrocatalysts for Methanol Oxidation Reaction[END_REF], but also increases the yield of aromatic compounds like vanillin, 3-methylbenzaldehyde and apocynin [START_REF] Ghahremani | Electrochemical oxidation of lignin for the production of valueadded chemicals on Ni-Co bimetallic electrocatalysts[END_REF]. However, the separation and recovery of these various products in the anolyte remains a technological bottleneck. One possible strategy is to implement an in-situ selective extraction of low molecular weight products by an aqueous deep eutectic solvent associated with an extractant phase (e.g., methyl isobutyl ketone) to avoid their over-oxidation [START_REF] Marino | Emulsion electro-oxidation of kraft lignin[END_REF]. Another approach, proposed by Schmitt et al., is based on the absorption of the target fractions by a strongly basic anion exchange resin [START_REF] Schmitt | Highly selective generation of vanillin by anodic degradation of lignin: a combined approach of electrochemistry and product isolation by adsorption[END_REF].

Finally, the membrane technology is probably the most promising, due to its compact and modular approach and the avoidance of additional solvent and extractant phase. In this process, a filtration membrane can be integrated, like an AEM, in a 3-chamber electrolyzer [START_REF] Stiefel | Controlled depolymerization of lignin in an electrochemical membrane reactor[END_REF] (Figure 2a-b) or used downstream of the lignin electrolyzer [START_REF] Stiefel | An integrated electrochemical process to convert lignin to value-added products under mild conditions[END_REF] (Figure 2c) to separate the unreacted lignin (retentate) in the anolyte from the low molecular weight fractions (permeate). For instance, Figure 2d shows the time evolution of the relative molecular weight of the lignin electrooxidation products in an AEM using a Ni-based anode (indicating enhanced lignin depolymerization with increased electrical current), while Figure 2e shows a typical chromatogram of both retentate and permeate fractions, demonstrating the ability of the ultrafiltration membrane to extract low-molecular weight compounds in the permeate stream [START_REF] Stiefel | An integrated electrochemical process to convert lignin to value-added products under mild conditions[END_REF].

ii) Lignin electrooxidation above 100°C

Operating an electrolyser at temperatures above 100°C provides advantages such as better oxidation kinetics and more favourable thermodynamic conditions. The group of Hibino at the Nagoya University was the first to explore lignin electrolysis between 100 and 200°C, using a PEM electrolyser with a H +conducting Sn0.9In0.1P2O7-polytetrafluoroethylene (PTFE) membrane [START_REF] Hibino | Hydrogen Production by Direct Lignin Electrolysis at Intermediate Temperatures[END_REF][START_REF] Hibino | the use of a functionalized carbon black as anode for the direct electrolysis of a wide variety of raw biomass (cellulose, starch, lignin, protein, lipid, wastes of bread, cypress, rice chaff) in acid[END_REF][START_REF] Hibino | The authors explored the use of a functionalized carbon black as anode for the direct electrolysis of the cellulose and lignin[END_REF]. Lignin was dissolved in H3PO4 and impregnated on the anode. In a batch cell configuration (Figure 3a), lignin could be electrooxidized from 0.25 V at 200°C on Pt/C and 0.1 V at 150°C on PtFe/C [START_REF] Hibino | Hydrogen Production by Direct Lignin Electrolysis at Intermediate Temperatures[END_REF], a performant electrocatalyst that also stood out in direct cellulose fuel cells [START_REF] Hibino | High Performance Anode for Direct Cellulosic Biomass Fuel Cells Operating at Intermediate Temperatures[END_REF]. Faradaic efficiency values of 100% towards H2 evolution on the cathode and 83-91% towards CO2 formation on the anode were determined by mass spectrometry, regardless of the temperature. C4-C7 aromatic and aliphatic molecules were further detected by liquid chromatography-mass spectroscopy after thermal treatment of the lignin-H3PO4 solution at 200ºC [START_REF] Hibino | Hydrogen Production by Direct Lignin Electrolysis at Intermediate Temperatures[END_REF]. During continuous operation at 20 mA cm -2 and 150°C, a voltage of only 0.57 V was required after 30 min using the PtFe/C anode, corresponding to a low electric energy consumption rate of 1.36 kWh per Nm 3 H2 (Table 1), although the energy for heating was not considered. More recently, the same group has investigated the electrochemical oxidation of raw biomass dissolved in H3PO4, from model molecules like cellulose, starch, lignin, protein and lipid [START_REF] Hibino | the use of a functionalized carbon black as anode for the direct electrolysis of a wide variety of raw biomass (cellulose, starch, lignin, protein, lipid, wastes of bread, cypress, rice chaff) in acid[END_REF] to more complex lignocellulosic molecules like wastes of bread, cypress, rice chaff [START_REF] Hibino | the use of a functionalized carbon black as anode for the direct electrolysis of a wide variety of raw biomass (cellulose, starch, lignin, protein, lipid, wastes of bread, cypress, rice chaff) in acid[END_REF] and even newspaper [START_REF] Hibino | The authors explored the use of a functionalized carbon black as anode for the direct electrolysis of the cellulose and lignin[END_REF], both in the previous batch cell configuration (Figure 3a) and in a flow-through configuration equipped with a syringe feeder (Figure 3b). Using a metal-free anode consisting of a carbonyl-functionalized mesoporous carbon, raw biomass was electro-oxidized at cell voltages lower than 0.5 V at 150ºC, reaching current densities up to 0.3 A cm -2 at 1 V and producing mainly CO2 and NO2 (from proteins) at the anode (Figures 3c and3d) [START_REF] Hibino | the use of a functionalized carbon black as anode for the direct electrolysis of a wide variety of raw biomass (cellulose, starch, lignin, protein, lipid, wastes of bread, cypress, rice chaff) in acid[END_REF][START_REF] Hibino | The authors explored the use of a functionalized carbon black as anode for the direct electrolysis of the cellulose and lignin[END_REF]. Electrochemical performances were dependent on the main functional groups (e.g., carbonyl groups in cellulose and starch were more reactive than carboxyl groups in proteins) and on the acid-solubility (lignin and lipids being less soluble). These studies demonstrate the possibility of electrolyzing real biomass without any noble metal at moderate temperatures (100-200ºC) in acidic media, resulting in lower electric energy consumption (Table 1). However, some bottlenecks remain such as sluggish kinetics, deactivation issues and heating energy requirements. In addition, above 100°C, lignin and other raw biomass are mainly electrooxidized into CO2 (Fig. 3d) to the detriment of value-added chemicals. On the other hand, high-temperature electrolysis in alkaline conditions seem to promote the electrooxidation of lignin into vanillin: for instance, the group of Waldvogel at University of Mainz recently proved that the selective depolymerization of lignin is possible in alkaline media at 160ºC using simple Ni foam electrodes in a batch cell configuration at current densities of 5-40 mA cm -2 (2-3 V) [START_REF] Zirbes | High-Temperature Electrolysis of Kraft Lignin for Selective Vanillin Formation[END_REF]. Vanillin and acetovanillone yields of 2.0-4.2 wt.% and 0.2-1.2 wt.%, respectively, were obtained depending on the lignin source and the operation conditions.

Conclusions

Low temperature lignin electrolysis has been demonstrated with energy inputs in the 2.5 -4.5 kWh per Nm -3 H2 range on electrodes made of non-noble metal compounds (Ni, Co, Ti, Pb) in alkaline conditions, with the selective production of H2 at the cathode and the generation of valuable aromatic molecules at the anode. Furthermore, lignin conversion can be more efficient and less demanding in electrical energy at 150-200°C. Importantly, at these temperatures, lignin is mostly converted in acidic conditions to CO2, reducing the added value brought by the production of platform aromatic compounds observed at low temperature. However, in alkaline conditions, the generation of aromatics seems to increase with the temperature on Ni-based electrodes. While improvements have been made regarding the energy efficiency of the process, its kinetics remain lower than the ones involved in traditional water electrolysis by several orders of magnitude. If low current densities have been ascribed to the fouling of electrodes and blocking of active sites by lignin, in-depth mechanistic studies are still lacking as well as a thorough analysis of the anodic products obtained in flow-through lignin electrolysis cells. This is partly due to the extreme chemical complexity of the molecule at hand and the wide variety of reaction and side products, requiring the development of advanced in-situ and operando analytic tools to unravel the molecules interaction with catalytic sites under operating conditions. Thankfully, significant progress is currently being made on this front, which gives hope for a rapid improvement in the understanding and efficiency of lignin electrolysis in the coming years. [29] R. Ghahremani, F. Farales, F. Bateni, J.A. Staser, Simultaneous Hydrogen Evolution and Lignin Depolymerization using NiSn Electrocatalysts in a Biomass-Depolarized Electrolyzer, Journal of The Electrochemical Society. 167 (2020) 43502. ** The authors studied the effect of Sn-doping in Ni catalysts used in an AEM cell for the electrolysis of a biorefinery lignin at room temperature. An optimum composition of Ni3Sn1 led to the highest electrocatalytic performance, which was directly linked to an enhanced electrochemical surface area.

Figure 1 .

 1 Figure 1. a) Schematic representation of the lignin structure, highlighting monolignols: sinapyl alcohol

Figure 2 .

 2 Figure 2. a) Scheme and b) cross section of the setup integrating the alkaline lignin electrolysis and membrane separation processes, where NFM stands for nanofiltration membrane; Reprinted with permission from [19]. c) Scheme of the setup comprising an alkaline lignin electrolyzer and a downstream membrane module; d) relative molecular weight of kraft lignin after electrolysis in an AEM with a Ni-based anode; e) example of size exclusion chromatogram of the retentate and the permeate in configuration c). Reprinted with permission from [49].

Figure 3 .

 3 Figure 3. Schemes of a) batch and b) flow-through cell configurations for intermediate-temperature electrolysis of H3PO4-dissolved lignin; c) I-V curves of the electrolysis of various model biomass molecules at 150ºC in a batch cell. Reprinted with permission from Ref. [50]. d) Evolution of cell voltage, H2 and CO2 production rates with time during continuous electrolysis of newspapers at 175ºC in a batch cell for different cell voltages. Anode: carbonyl-group functionalized mesoporous Kerjen black carbon, membrane: Sn0.9In0.1P2O7-PTFE, cathode: Pt/C. Reprinted with permission from Ref. [51].

Table 1 .

 1 Electrocatalytic performance of anodes tested for direct lignin electrolysis for H2 production.

	Anode : Catalyst / support	Cell configuration	Operation conditions	T (ºC)	Current density (mA cm -2 )	Cell voltage (V)	Time (h)	H2 production (mL min -1 )	H2 FE (%)	Electric energy (kWh Nm -3 ) consumption	Ref.
	Ni / Ti Ni3Sn1 / Ti	AEM cell Cathode: Pt Membrane: FFA-3	Biorefinery lignin (10 g L -1 ) in 1 M NaOH	RT	13.1 16.0	1.60 1.60	--	1.00 1.20	99.0 99.5	3.49 3.55	[29]
	NiCo-TiO2 (1:3) / Carbon paper	AEM cell Cathode: Pt Membrane: FFA-3	Biorefinery lignin (50 g L -1 ) in 1 M NaOH	RT	10.0 20.0 30.0	1.60 1.67 1.72	24.00 24.00 24.00	0.74 1.49 2.26	99.0 100.0 101.0	3.91 4.03 4.12	[20]
	NiCo/TiO2 / Carbon paper PbO2/MWNTs / Carbon paper	AEM cell Cathode: Pt Membrane: FFA-3-50	Kraft lignin (10 g L -1 ) in 1 M NaOH	RT	20.0 30.0 20.0 30.0	1.98 2.15 1.87 1.96	0.05 0.04 0.05 0.04	1.52 2.28 1.52 2.28	98.5 99.4 98.5 97.2	4.34 4.73 4.15 4.41	[28]
	Ti/PbO2	Batch AEM cell Cathode: Pt Membrane: FFA-3-50	Sodium lignosulfonate (10 g L -1 ) in 1 M NaOH	60	0.4	1.80	5.00	0.02 a	-	4.31 a	[39]
	Ni(OH)2/C (22 wt.% Ni) / Carbon cloth	AEM cell, Cathode: Pt/C Membrane: FAA-3-50	Kraft lignin (10 g L -1 ) in 1 M KOH	80	1.7 7.5	1.10 1.50	1.00 1.00	0.30 a 1.30 a	̴ 100 ̴ 100	2.63 a 3.59 a	[21]
	Pt/C (40 wt.% Pt) PtFe/C	Batch cell Cathode: Pt/C Membrane: Sn0.9In0.1P2O7	H3PO4-impregnated Lignin (wt. ratio 1:2.8)	150	20.0 20.0	0.64 0.57	0.50 0.50	0.28 a 0.28 a	̴ 100 ̴ 100	1.53 a 1.36 a	[27]
	a Values calculated by assuming a H2 faradaic efficiency (FE) of 100%.

, although at slightly higher potentials than Ni-based catalysts employed in other works by the same group.

Acknowledgments

The authors thank the European Union's Horizon Europe research and innovation programme under grant agreement No 101070856 ELOBIO for funding.

Conflict of interests

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this article.


Madeleine Abernot

Corentin Delacour

Ahmet Suna

J Marty Gregg

Siegfried Karg

Aida Todri-Sanial

Two-Layered Oscillatory Neural Networks with Analog Feedforward Majority Gate for Image Edge Detection Application

Keywords: Oscillatory Neural Networks, Image Edge Detection, Majority Gate, Feedforward

The increasing volume of smart edge devices, like smart cameras, and the growing amount of data to treat incited the development of light edge Artificial Intelligence (AI) solutions with neuromorphic computing. Oscillatory Neural Network (ONN) is a promising neuromorphic computing approach which uses networks of coupled oscillators, and their inherent parallel synchronization to compute. Also, ONN phase computing allows to limit voltage amplitude and reduce power consumption. Low-power, fast, and parallel computation properties make ONN attractive for edge AI. In state-of-theart, ONN is built with a fully-connected architecture, with coupling defined from unsupervised learning to perform autoassociative memory tasks, like with Hopfield Networks. However, to allow ONN to solve beyond associative memory applications, there is a need to explore further ONN architectures. In this work, we propose a novel architecture of cascaded analog fully-connected ONNs interconnected with an analog feedforward majority gate layer. In particular, we show this architecture can solve image edge detection task using two fully-connected ONN layers. This is, to our best knowledge, a first analog-based solution to cascade two fully-connected ONNs.

I. INTRODUCTION

With the proliferation of edge devices in numerous domains, for example cameras for smart cities, medical assistance, and others, there is a tremendous amount of data to treat [START_REF] Luckey | Artificial Intelligence Techniques for Smart City Applications[END_REF] [START_REF] Baran | A smart camera for the surveillance of vehicles in intelligent transportation systems[END_REF]. Artificial Intelligence (AI) with the development of Artificial Neural Networks (ANNs) is an efficient solution to solve complex problems requiring large datasets, however, it is often performed in the cloud as it requires a lot of computational resources for learning and inference [START_REF] Sun | Edge-Cloud Computing and Artificial Intelligence in Internet of Medical Things: Architecture, Technology and Application[END_REF]. Using cloud computing, data is transferred over the cloud inducing slow latency and high energy consumption. Thus, current research concentrates on how to implement AI and ANNs at the edge with limited resources and energy consumption respecting real-time constraints [START_REF] Plastiras | Edge Intelligence: Challenges and Opportunities of Near-Sensor Machine Learning Applications[END_REF].

A solution takes inspiration from biology to design neuromorphic computing techniques, like Spiking Neural Networks [START_REF] Schuman | Opportunities for neuromorphic computing algorithms and applications[END_REF] [START_REF] Christensen | roadmap on neuromorphic computing and engineering[END_REF]. In this work, we focus on another promising neuromorphic paradigm with Oscillatory Neural Networks (ONN) [START_REF] Csaba | Coupled oscillators for computing: A review and perspective[END_REF][8] [START_REF] Todri-Sanial | How Frequency Injection Locking Can Train Oscillatory Neural Networks to Compute in Phase[END_REF] inspired by brain oscillations. ONNs are networks of coupled oscillators computing with inherent parallel phase synchronisation of coupled oscillators. Phase computing encodes information in the phase relationship among oscillators. It allows to reduce power consumption by limiting the voltage amplitude. Low power and fast parallel ONN computing makes it attractive for edge AI [START_REF] Delacour | Energy-Performance Assessment of Oscillatory Neural Networks based on VO2 Devices for Future Edge AI Computing[END_REF].

ONN shows efficient auto-associative memory properties with a fully-connected (FC) architecture configured with unsupervised learning [START_REF] Hoppensteadt | Pattern recognition via synchronization in phase-locked loop neural networks[END_REF], similar to Hopfield networks, see Fig. 1. Auto-associative memories can solve pattern recognition applications. However, to enlarge ONN application scope, it is important to explore alternative ONN architectures. Recently, [START_REF]Empty for blind review[END_REF] proposed to use ONN with a two-layer bidirectional architecture for hetero-association to perform image edge detection. Similarly, authors in [START_REF]Empty for blind review[END_REF] adapted the hetero-associative ONN from [START_REF]Empty for blind review[END_REF] to a feedforward (FF) ONN and were able to improve image edge detection performances. However, both works use digital ONN implementations on FPGA. FF-ONN is not possible with analog design due to natural bidirectional coupling among oscillators. Another approach [START_REF] Velichko | A Model of an Oscillatory Neural Network with Multilevel Neurons for Pattern Recognition and Computing[END_REF] proposed a first analog multi-level ONN to perform pattern recognition, however they use frequency computing with pulse-type ONN.

In this work, we propose a novel architecture to cascade two FC-ONNs configured for pattern recognition with a FF layer based on an analog Majority Gate (MG) function. We show this architecture is also applicable to image edge detection application. To our best knowledge, it is a first attempt to cascade two analog FC-ONNs. The main contributions of this work are i) the development of a FF layer based on an analog MG function, a FF-MG layer, to connect two FC-ONNs configured for pattern recognition, and ii) the adaptation of the solution to solve image edge detection application.

The paper is organized as follows. Section II presents the ONN phase computing paradigm, and its state-of-the-art architectures and applications. Section III describes our Fig. 1: FC-ONN configured for associative memory novel architecture using FF-MG layers to interconnect two FC-ONNs. Section IV explains how to configure the system to perform image edge detection. Section V shows results obtained of our cascaded FC-ONN architecture on the image edge detection application and compares with previous works. Finally, Section VI discusses the advantages and limitations of our FF-MG layer solution.

II. OSCILLATORY NEURAL NETWORKS (ONNS)

ONN is a neuromorphic computing paradigm taking inspiration from brain oscillations. In this Section, we present the ONN computing model and its state-of-the-art architectures and applications.

A. ONN Computing Paradigm

ONNs are networks of coupled oscillators emulating brain oscillations and using the intrinsic phasesynchronization of coupled oscillators to compute. Using phase-computing ONNs, information is encoded in the phase relationship among oscillators. For example, for binary information, a logic '0' is encoded with a 0° phase, while a logic '1' is encoded with a 180° phase. ONN computation starts by phases of each oscillator in the network from input data. Then, phases evolve depending on the coupling between oscillators, and stabilizes to a final phase state. The evolution of phases corresponds to the minimization of an intrinsic energy parameter, like in attractor networks [START_REF] Buhmann | Associative memory with high information content[END_REF]. The final phase state gives the network output information. Thus, the coupling among oscillators, defined by learning, is the main parameter to solve specific tasks efficiently.

B. ONN Architectures and Applications

In state-of-the-art, ONN is used with a FC architecture, configured with unsupervised learning, to perform autoassociative memory tasks, like Hopfield networks, see Fig. 1. In this case, the network memorizes patterns based on its couplings and evolves to a learnt pattern when initialized with a corrupted input information. FC-ONN configured for pattern recognition can be used in various applications [16][17]. However, the FC-ONN architecture first requires large amount of coupling elements, increasing quadratically with the number of neurons. The number of synaptic elements is N(N-1)/2 for a network of N neurons making it hard to implement at large scale. Additionally, solving associative memory tasks is interesting but the unsupervised learning is often limiting the network capacity, meaning the number of patterns a network can learn and retrieve efficiently. Thus, there is a need to explore other architectures and applications applicable to ONNs.

Recently, two-layer ONN architectures were introduced with bidirectional and feedforward connections between layers, considering no connections among oscillators of the same layer [START_REF]Empty for blind review[END_REF] [START_REF]Empty for blind review[END_REF]. In both works, authors use their twolayer ONN to solve image edge detection. Additionally, in these works, the two-layer ONNs are implemented digitally on FPGA. However, using analog implementation, it is not possible to create a FF-ONN as coupling among oscillators is by-default bidirectional.

III. ANALOG FF-MG LAYERS FOR CASCADED FC-ONNS

In this work, we propose a solution to cascade two FC-ONNs with an analog-based FF-MG layer. Section III. A. presents the analog FC-ONN and its processing. And Section III. B. describes the analog FF-MG layer used to cascade two FC-ONNs.

A. Analog FC-ONN

In this work, we consider CMOS relaxation oscillators coupled with resistive coupling, see Fig. 2. The resistive couplings are mapped from the weights generated with unsupervised learning rules [START_REF] Delacour | Mapping Hebbian Learning Rules to Coupling Resistances for Oscillatory Neural Networks[END_REF]. Once the coupling is configured and the circuit is mapped correctly, we initialize each oscillator. The initialization consists of applying a VDD_osc to each oscillator. The phase-shift is encoded in the delay of activation of the VDD_osc. For example, if we want to initialize two oscillators with 180° phase shift, we will activate VDD_osc1 at t=0, and activate VDD_osc2 at t=T/2, with T the period of oscillation. After initialization, each VDD_osc stays active so oscillators' phases evolve until stabilization. Stabilization is detected after numerous period cycles with stable phases. The final phase state corresponds to the output information of the FC-ONN.

B. Analog FF-MG layer

In this work, we propose a solution to cascade two FC-ONNs. Thus, after the first FC-ONN layer stabilization, we use the oscillating outputs as input of the FF-MG layer, as shown in Fig. 2. In Fig. 2, two FF-MG layers are represented, each layer taking as input three oscillating signals from the first FC-ONN layer, performing MG function, and using the two FF-MG output as input of a second-layer FC-ONN.

The FF-MG layer contains various levels. A first level of analog buffers is necessary to send the first-layer FC-ONN outputs to the FF-MG layer without impacting the FC-ONN behavior. Then, the second level uses oscillations from analog buffers and performs a MG function with a summing amplifier. In Fig. 2, each MG takes three oscillating signals as input and outputs a signal with phase corresponding to the majority phase of the three input oscillations. The third level is a non-linear amplifier which saturates the signal to replicate an analog to digital conversion. From this digital signal, the fourth level synchronizes the various MG layers together. To do so, a latch is placed in between the linear amplifier output and the next-layer oscillator input. When the latch is enabled, the VDD_osc of the oscillator from next layer is activated following the phase-shift given by the linear amplifier. The enable signal Ven is set in the same moment for each FF-MG layer to synchronize them for the next FC-ONN layer, see example in Fig. 3.

IV. APPLICATION TO IMAGE EDGE DETECTION

We apply our architecture to perform image edge detection. Image edge detection is an important image processing task used as first step of many broader problems, like image segmentation, or object detection [START_REF] Lowe | Object recognition from local scale-invariant features[END_REF] [START_REF] De | An image segmentation method based on the fusion of vector quantization and edge detection with applications to medical image processing[END_REF]. Image edge detection algorithms mainly use 3x3 convolutional filters to scan an image and assign a gradient to each pixel of the image which indicates if an edge is detected. As in [START_REF]Empty for blind review[END_REF][13], we try to solve image edge detection by replacing convolutional filters with our proposed architecture. Recently, [START_REF]Empty for blind review[END_REF] proposed a solution using a FC-ONN trained to perform pattern recognition with 4 patterns representing 4 edges (horizontal, vertical, and diagonals), and using a postprocessing algorithm to define if an edge is detected or not. By analyzing their solution, we noticed that the postprocessing can be adapted as a combination of FF-MG layers. Thus, we propose to use our analog FF-MG solution instead of a post-processing using the same first-layer FC-ONN from [START_REF]Empty for blind review[END_REF] in order to build an analog-based all-in-one architecture. The first FC-ONN is trained with 4 patterns representing the 4 main edges (horizontal, vertical, and diagonals), using the Hebbian learning rule [START_REF] Morris | The Organization of Behavior[END_REF] see Fig. 4.a). Then, when the first FC-ONN is stable, we use its output as input of 4 FF-MG layers to detect each edge, see Fig. Note, the second-layer FC-ONN does not have any connections between oscillators. It can be considered as a FC-ONN with 0-weights coupling. We test and validate our solution with a hardware board for two edges, horizontal and vertical, and we generalize for four edges using simulations.

V. RESULTS

This section presents results of our analog-based FF-MG architecture to cascade two FC-ONN adapted to image edge detection. Fig. 5 shows results of our image edge detection solution on the 'cameraman' large scale image. Visually, it shows that we can detect edges efficiently. It is compared with a digital FF-ONN applicable for image edge detection using an FPGA implementation [START_REF]Empty for blind review[END_REF]. The digital FF-ONN does not cascade two FC-ONN but considers an input layer that feeds an output layer without connections among neurons in the same layer. Table I shows the Jaccard Similarity Coefficient (JSC) metric that uses the state-of-theart Canny algorithm [START_REF] Canny | A Computational Approach to Edge Detection[END_REF] as ground truth (GT), and is compared with the state-of-the-art Sobel algorithm [START_REF] Sobel | A 3×3 isotropic gradient operator for image processing[END_REF], as well as the digital FF-ONN [START_REF]Empty for blind review[END_REF]. Table I shows that the two cascaded analog FC-ONN using a FF-MG layer miss some important edges, and does not place correctly all detected edges.

Another, important parameter for image edge detection algorithm is the latency. In order to compare the FF-ONN [START_REF]Empty for blind review[END_REF] solution meaningfully with our analog FC-ONN, we reproduce our analog system in digital. To do so, we use a digital FC-ONN configured for pattern recognition of the four edge patterns, see Fig. 4.a). And we connect four FF-ONNs with weights equal to 1 to replace the analog FF-MG layer. The digital FF-ONN with weights equal to '1' reproduces the MG function. Both analog and digital systems obtain the same precision results. Table II reports on latency of our solution (analog and digital implementation) compared to digital FF-ONN from [START_REF]Empty for blind review[END_REF]. The analog FC-ONN stabilizes in 4-5 oscillation cycles while the digital FC-ONN only requires 3-4 cycles. On the other side, the digital FF-ONN, and the analog FF-MG layers stabilize in only 1 to 2 cycles. Thus, the cascaded FC-ONNs solution requires the stabilization of a FC-ONN and a MG layer, whereas the FF-ONN only requires to wait for the digital FF-ONN stabilization, hence the latency of our solution is longer. Note, we consider a parallel execution of the four MG layers to speed up the process and the oscillating frequency is higher in analog than in digital.

This work proposes an analog solution to cascade two FC-ONN using a MG activation function, and shows it can solve image edge detection task, even though it has limited precision, and longer processing time.

VI. DISCUSSION

This work introduces an analog-based architecture to cascade two analog FC-ONNs using a FF-MG activation function. We show this novel architecture is capable of performing image edge detection task. However, it is less precise, detects less edges with higher latency than previous FF-ONN work.

Nevertheless, this work introduces a novel FC-ONN layered architecture which can allow ONN to explore novel applications. The proposed architecture is modular; thus, it can be adapted to include more than two FC-ONN layers, with modularity in input and output data. Furthermore, in this paper, we only consider an analog MG activation function. However, we can replace the FF-MG with other activations. For example, in [START_REF] Amarel | Majority Gate Networks[END_REF] [START_REF] Goto | The Parametron, a Digital Computing Element Which Utilizes Parametric Oscillation[END_REF], authors have shown MG functions to construct different operations such as AND, OR, and XOR. Even though we applied our architecture to image edge detection as commonly explored in the state-of-the-art [START_REF]Empty for blind review[END_REF], however, applying FF-MG layers, it is, in principle, compatible with numerous applications requiring at least two FC-ONN layers. However, it requires further investigations to train such a system for a specific task.

Finally, the FF-MG layer is almost fully analog, apart from the digital latch level. Using a fully-analog system is advantageous for analog computing applications, for example for smart sensors. In our design, the latch takes care of the synchronization of the different FF-MG layers. Also, it limits the power consumption by activating the second FC-ONN layer once the first FC-ONN layer is over. However, note that if all FF-MG inputs are synchronized, for example if they are part of the same FC-ONN, then input signals to second FC-ONN should also be synchronized. Thus, our FF-MG layer can adapt to a fully-analog system.

VII. CONCLUSION

This paper presents a first solution to cascade analog fully-connected ONNs with an analog feedforward majority gate layer. This is, to the best of our knowledge, a first attempt to achieve analog feedforward ONN by cascading two fully-connected ONNs. More particularly, we use an analog feedforward majority gate layer to connect two fullyconnected ONNs. We show this novel architecture can be adapted to perform image edge detection. In this case, a firstlayer fully-connected ONN is trained for pattern recognition with four 3x3 images representing edges (horizontal, vertical, and diagonals). Then, four feedforward majority gate layers are used to post-process the output of the first fullyconnected ONN and detect edges. Even though performances are not competitive compared with state-of-the-art edge detection algorithms, our novel modular architecture based on cascaded fully-connected ONNs enlarges the scope of analog ONN applications.

ACKNOWLEDGMENT

Empty for blind review.

Fig. 2 :

 2 Fig.2: Schematic of two cascaded FC-ONNs with two MG FF layers. VDD = 3V.

  4.b).

Fig. 3 :

 3 Fig.3: Experimental results of a) internal signals for 2 FF-MG layers. Vmgo1 is the output of the output amplifier, Ven is the enabling signal common to both FF-MG layers, and VDDosc are input voltages of each oscillator from second layer. b) Output oscillating signals of oscillators from second layer.

Fig. 4 :

 4 Fig.4: Cascaded FC-ONN configured for image edge detection. a) Weight configuration of the first-layer FC-ONN. b) Architecture of the second layers for each egde detection.

Fig. 5 .

 5 Fig.5. a) Example of FC-ONN behavior for two input images. b) Results of our simulated cascaded FC-ONNs configured for image edge detection on the black and white 'cameraman' image. c) and d) Simulation results of the FF-MG layer for two images.

TABLE I

 I

	: PRECISION OF CASCADED ANALOG FC-ONNS ON
	IMAGE EDGE DETECTION ON THE 'CAMERAMAN' IMAGE
	COMPARED WITH CANNY GROUND TRUTH (GT)
	GT: Canny	Sobel	Dig. FF-ONN [13]	This work
	JSC	0.5204	0.4388	0.1866
	Overlapping	7277	7433	2021
	Union		13983	16941	10832
	TABLE II: LATENCY OF OUR SOLUTION COMPARED TO
	PREVIOUS DIGITAL FF-ONN [13], AND ESTIMATION FOR LARGE-
			SCALE IMAGES.
	Latency	Digital FF-	This work -analog	This work -digital
		ONN [13]	Fa=3 MHz	Fd=2.7 MHz
	3x3	1.15 us		FC: 1.67 us	FC: 1.42 us
				FF-MG: 0.67 us	FF: 1.15 us
	28x28	0.78 ms		1.83 ms	2.01 ms
	512x512	301 ms		613 ms	674 ms