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HARVARD UNIVERSITY

APPLIED COMPUTATION 297R

CAPSTONE PROJEC T

Fast Algorithms for Membrane and Synapse

Detection

Authors:

Hallvard Moian NYDAL

Cole DIAMOND

Rapha

el PESTOURIE

Mina NASSIF

Professor:

Pavlos PROTOPA PA S

Project Parnter:

Verena KAYNIG -FITTKAU

Teaching Fellow:

Thouis Ray JONES

May 15, 2015

Fast Algorithms for Membrane and Synapse

Detection

Hallvard Moian Nydal

Institute for Applied

Computational Science

Harvard University

Cole Diamond

Institute for Applied

Computational Science

Harvard University

Rapha

el Pestourie

School of Engineering

and Applied Science

Harvard University

Mina Nassif

Institute for Applied

Computational Science

Harvard University

Abstract—Connectomics is the study of the structural

and functional connections among brain cells. By com-

paring diseased connectomes and healthy connectomes,

physicians and researchers alike can gain valuable insight

into neurodegenerative disorders like Alzheimers. As au-

tomated approaches to scanning-electron microscopy at

nano-resolution have yielded increasingly larger data-sets,

the need for scalable data processing has become crucial.

Using a set of manually-annotated images, we perform

binary classiﬁcation of the pixels to detect cell membranes

and synaptic clefts. Compared to state-of-the-art pixel-wise

prediction method, we show that predicting multiple pixels

in batches cuts training and prediction time by a factor of

100, while sacriﬁcing little by way of predictive accuracy.

Index Terms—Connectomics, Convolutional Neural Net-

works, Window Prediction

I. INTRODUCTION

The connectome is the wiring diagram of the

brain and nervous system. Mapping the network of

neurons in organisms is vital for discovering the

underlying architecture of the brain and investigat-

ing the physical underpinning of cognition, intelli-

gence, and consciousness. It is also an important

step in understanding how connectivity patterns are

altered by mental illnesses and various pathologies.

Advancements in scanning electron microscopy has

made feasible the 3D reconstruction of neuronal

processes at the nano-scale (see ﬁgure 1).

However, connectomics at the microscale has

proven to be a trying task. With manual annotation

and reconstruction, mapping cannot be completed

within a realistic time frame [1,2]. As automated ap-

proaches to scanning-electron microscopy at nano-

resolution have yielded increasingly larger data-sets,

there is strong interest in ﬁnding more scalable

Fig. 1: Automated Reconstruction of Neuronal Processes.

Image Credit: Kaynig et al. [5]

approaches to automating identiﬁcation of neurons

and synapses.

The main contribution of our research is a fast and

scalable algorithm for detecting membrane edges

and synapses. By predicting multiple pixels simul-

taneously, we are able to cut training and prediction

time while sacriﬁcing little accuracy.

II. PRIOR WORK

Of seminal importance in the realm of large-scale

reconstruction of neuron mappings is the work done

by Kaynig et al. [5]. The authors propose a pipeline

for automatically reconstructing neuronal processes

from large-scale electron microscopy image data.

The pipeline is represented graphically below. Our

focus is on the stage of the pipeline concerning

recognition of cell membranes and synapses.

The proposed pipeline is a viable solution for

large-scale connectomics, although training time is

prohibitively long [5]. From critical path analysis,

we see that the bottleneck of training occurs during

the membrane classiﬁcation stage. In the implemen-

tation by Kaynig et al., each pixel is classiﬁed.

Fig. 2: Complete workﬂow for large-scale neuron reconstruc-

tion. Image Credit: Kaynig et al. [5]

Drawing from the work of Hinton in road classiﬁ-

cation, predicting patches of pixels simultaneously

may improve the throughput of a system with minor

compromise to accuracy [6]. We also draw from

Hinton in applying Gaussian thickening to edges to

improve predictive accuracy.

Recently, synapses have become the focus of

classiﬁcation and region segmentation efforts. An

example synapse is shown in ﬁgure 3. In a bench-

mark study by Becker et al., a high Jaccard index

for different values of ’exclusion zone thickness’

for synapse classiﬁcation was achieved [4]. Our

work attempts to apply batch prediction methods

to membrane detection as well as synapse synapse

detection, where we will use Becker et al. as a point

of comparison.

Fig. 3: A synapse’s morphology is marked by vesicles, a

synaptic cleft and a post-synaptic region.

III. DATA SANITIZATION

In order to augment the predictive power of our

models, we pre-process our training, testing and

validation data using a variety of techniques. Pre-

processing reduces noise from the original data and

underscores important features. We employ seven

steps in our pre-processing pipeline: feature normal-

ization, edge-detection, stochastic rotation, adaptive

histogram equalization, shufﬂing, and dataset bal-

ancing.

A. Feature Normalization

The ﬁrst step of our feature-normalization proce-

dure is reshaping our images to 1024 ⇥ 1024 pixels.

Therefore, we perform standardization along the

columns where we subtract the mean of the column

and divide by its standard deviation, z =

xµ



B. Edge-Detection

For cell-membrane detection, we use edge-

detection to binarize our data. To do so, we perform

a 2D convolution using the scharr kernel [10]. We

also utilize edge-thickening as in Hinton [6] to

reduce the sparsity of the feature. To do so, we grow

the edges by converting all pixels in a neighborhood

of an existing edge to edge pixels. Thereafter, we

apply a gaussian blur to our data to make our

convolutional neural network more robust to noise.

C. Stochastic Rotation

Rowley et al. showed that stochastic rotations

can introduce rotation invariance [2]. In order to

introduce rotation invariance, we randomly rotate

our training data by 90, 180 or 270 degrees.

D. Shufﬂing

To avoid over-ﬁtting, we shufﬂed our data using

two different schemes. At ﬁrst, we permuted the

order of the sub-windows which we use for training

to ensure that we did not train on the same sample

twice within a batch. To simplify matters, we then

decided to randomly sample the training data to use

in our batch. Since the probability that we train

on the same input twice within a batch is small as

the amount of data grows, we opted for the latter,

simpler shufﬂing scheme.

E. Adaptive Histogram Equalization

Adaptive Histogram Equalization (AHE) is a pop-

ular and effective algorithm for improving local

contrast of the images which contain bright or dark

regions. An example

AHE differs from ordinary histogram equaliza-

tion in the respect that AHE computes several

Fig. 4: Comparison of an image without (left) and with

(right) adaptive histogram equalization. Image credit: Sujin

Philip sujin@cs.utah.edu

histograms, each corresponding to a distinct section

of the image; the method then uses the various

histograms to redistribute the lightness values of

the image. The algorithm of AHE is depicted in

Algorithm 1 in the appendix [15].

F. Data Balancing

For both synapse detection and cell-membrane

detection, it is important that the training set con-

tains an equal number of positive and negative ex-

amples. Accordingly, we center half of our training-

data on edges and synapses to effectively bias our

samples.

IV. CONVOLUTIONAL NEURAL NETWORKS

A. Background

Convolutional neural networks have become state

of the art in a wide range of machine learning

problems, including object recognition and image

classiﬁcation [9]. Convolutional neural networks

are able to achieve exceptional performance for a

multitude of different problems. Since convolutional

neural networks exhibit locality, translation invari-

ance, and hierarchical structure (see ﬁgure 5) , they

make for a natural pairing for object recognition.

The challenge with convolutional neural networks

is the relatively long prediction and training time.

A typical convolutional network architecture con-

sists of several stages. In the ﬁrst stage, a series of

convolutions are performed in parallel to produce a

set of presynaptic activations. In the detection stage,

each pre-synaptic activation is run through a nonlin-

ear activation function, such as the rectiﬁed linear

activation function. Thereafter, a pooling function

replaces the output of the net at a certain location

with a summary statistic of the nearby outputs.

Pooling makes features invariant from the location

Fig. 5: CNN’s can capture the natural hierarchy of images.

Image credit: Lee et al., ICML, 2009

in the input image, and activations less sensitive

to neural network structure. Often, an additional

stage is added implementing the max-out [18] and

dropout [19] techniques discussed in subsequent

sections. Figure 6 shows the architecture of a typical

convolutional network.

Fig. 6: A typical Convolutional Neural Network consist-

ing of six layers for MNIST classiﬁcation. Image credit:

https://engineering.purdue.edu/ eigenman

1) Rectiﬁed Linear Units: There are several

choices when it comes to activation functions in

neural networks. All are variations of the output of a

single node in a neural network, z

= x

+ b

where W 2 R

d⇥m⇥k

and b 2 R

m⇥k

are learned

parameters. In contrast to alternative activation func-

tions such as sigmodial functions, f(z)=(1+

exp(z))

1

and tanh functions, f (z)=tanh(z),

rectiﬁer linear units are unbound and can represent

any non negative real value.

Rectiﬁer linear units use the activation function

rect(z)=max(0,z). The activation function has

good sparsity properties due to having a real zero

activation value, and therefore, suffers less from Di-

minishing Gradient Flow. As a result, training time

decreases by a substantial factor. Alex Krizhevsky

et al. [16] decreases in training speed of up to

600 % on benchmark simulations on the ImageNet

data set Ergo, we use rectiﬁed linear units as the

activation function of choice for our convolutional

neural networks.

2) Dropout: The large number of neurons and

their associated connections makes neural networks

prone to over-ﬁtting. Dropout is a stochastic tech-

nique to reduce architectural dependence wherein

neurons and their incoming and outgoing connec-

tions are omitted with a predeﬁned probability.

Empirical results from Hinton et al. [19] shows that

dropout yields a signiﬁcant performance improve-

ment in predictive performance over a wide range

of data sets. Dropout can be understood as an efﬁ-

cient way to perform model averaging with neural

networks and to prevent complex co-adaptation on

the training data.

Fig. 7: In dropout training, units are temporarily removed

from a network, along with all its incoming and outgoing

connections. Image credit: Joost Van Doorm, J.vanDoorn-

1@student.utwente.nl

3) Maxout: In a convolutional network, a maxout

feature map can be constructed by taking the maxi-

mum across k afﬁne feature maps (i.e., pool across

channels). A single maxout unit can be interpreted

as making a piecewise linear approximation to an

arbitrary convex function (see ﬁgure 8). The maxout

activation function is designed to never have a

gradient of zero, allowing the network using maxout

and dropout to achieve a good approximation to

model averaging.

Fig. 8: Maxout activation function can implement the rec-

tiﬁed linear, absolute value rectiﬁer, and approximate the

quadratic activation function. Image credit: Goodfellow et al.

[18]

4) Root Mean Square Propagation: RMSProp

[21] uses a moving average over the root mean

squared gradients to normalize the current gradient.

Letting f

(✓t) be the derivative of the cost function

with respect to the parameters at time step t, ↵ be the

step rate, and  the decay term, we perform the fol-

lowing updates: r

=(1 )f

(✓

)

+ r

t1

; ⌫

t+1

↵

(✓

); ✓

t+1

= ✓

⌫

t+1

We use RMSProp instead

of stochastic gradient descent in our convolutional

neural network as it achieves greater classiﬁcation

performance on our dataset

B. Convolutional Neural Network Architecture

Our convolutional neural network consists of

twelve layers (see ﬁgure 9). For the input layer, we

take 64x64 pixel sub-windows from three images

slices located consecutively in the Z dimension.

Using image slices above and below the current im-

age slice enables us to leverage a three-dimensional

context for training and prediction.

1) Convolutional Filters: In our ﬁrst convolu-

tional layer, we convolve our input with 64 5x5

kernels using a stride length of 1. As a result, we

reduce our input dimensions to (64-5+1)x(64-5+1)

= 60x60. For convenience, we notate this layer as

C(64, 5, 1). Thereafter, we apply max-out to reduce

the number of ﬁlters from 64 to 32. In doing so,

we combine ﬁlters by taking the maximum for each

pixel across 2 consecutive ﬁlters, noted M(2). This

reduces the number of ﬁlters by a factor of 2.

Thereafter, we sub-sample a ﬁlter with 2x2 windows

and pool the maximum, noted P(2). This process,

known as max-pooling, further reduces the input

space to 30x30. Finally, we repeat this process using

a different set of parameters. Using the notation

C(number of ﬁlters, kernel size, length of stride),

M(maxout pieces), P(pooling window shape), the

Fig. 9: An illustration of the architecture of our convolutional network.

entire convolution sequence can be expressed as

C(64, 3, 1), M(2), P(2), and C(128, 3, 1), M(4),

P(2).

2) Fully-Connected Network: After the convo-

lution stage, our input is forwarded into a fully-

connected network. The network consists of one

hidden layer containing 1152 hidden units, and an

output layer containing 48 ⇥ 48 = 2304 units. The

output layer uses a logistic regression function to

output predictions on a 48 ⇥ 48 window of pixels.

3) Cost Function: Drawing from the work of

Rudin et al., we use total variation regulariza-

tion (TVR) for our cost-function to reduce noise

[22]. The TVR problem amounts to minimizing

the following discrete function over the signal y

E(x, y)+V (y). Since our signal is anisotropic, we

implement TVR as follows:

aniso

(y)=

i,j

i+1,j

 y

i,j

i,j+1

 y

i,j

i+1,j

 y

i,j

| + |y

i,j+1

 y

i,j

Lastly, we use root mean square propagation to

update our parameters. The entire architecture is

summarized in table I.

C. Implementation

Theano [17] is Python library for deﬁning, opti-

mizing and evaluating expressions involving high-

level operations on tensors. Developed to facilitate

research in Machine Learning, Theano is able to

TABLE I: Parameters of the Convolutional Deep

neural Network

Batch Size 30

Conv Layers 3

Conv Out Channels [64,64,128]

Conv Kernel Shape [5,3,3]

Kernel Stride [1,1,1]

Fully Connected Layers 1

Max Pooling [2,2,2]

Maxout [2,2,4]

Dropout [0.2,0.2,0.2,0.5]

Learning Rate 1.00E-07

Learning Rule RMSProp

Regularization coefﬁcient 1

attain speeds rivaling hand-crafted C implementa-

tions for problems involving huge amounts of data.

It can also surpass C on a CPU by many orders

of magnitude by leveraging GPU computing. That

said, Theano can also generate customized C code

for many mathematical operations. In combining as

aspects of a computer algebra system (CAS) with

aspects of an optimizing compiler, Theano is partic-

ularly useful for tasks in which complicated math-

ematical expressions are evaluated repeatedly and

evaluation speed is critical. Consequently, Theano

is the software of choice for implementing deep

learning solutions.

V. E VA L UAT I O N METHODOLOGY

A. Evaluating Cell Membrane Segmentation

1) Watershed Segmentation: For membrane de-

tection, we ﬁrst post-process the predicted synapses

using watershed segmentation. The watershed trans-

form treats its input as a topographic map, and

simulates ﬂooding over the topography with water.

The watershed regions are the parts of the map

which ”hold water” without spilling into other re-

gions. Figure 10 below illustrates the output of the

watershed segmentation on our predicted synapses.

Fig. 10: The watershed of an image is similar to the notion

of a catchment basin in a contour-relief map; a drop of water

follows the gradient of a hill, ﬂowing along a path to reach a

local minimum.

2) Variation of Information: Once we have ob-

tained a segmentation using the watershed algo-

rithm, we compare it to the ground-truth. To do so,

we use variation of information, which is deﬁned as

follows:

Suppose we have two partitions of an image A:

1) X - our predicted segmentation and 2) Y - the

labeled segmentation, or ground truth.

X = {X

,..,,X

},Y = {Y

,..,,Y

}

Let n =⌃

| =⌃

| = |A|,p

= |X

|/n,

= |Y

|/n, r

= |X

\ Y

|/n. Then, the variation

of information between the two partitions is:

VI(X; Y )=

i,j

[log(r

)+log(r

)]

B. Evaluating Synapse Prediction

For synapse prediction, we use the F1 score,

which is the harmonic mean of precision and re-

call. More formally, the F1 score is deﬁned as

=2·

precision·recall

precision+recall

. Moreover, precision is deﬁned

as the ratio of true positives to the sum of true

positives and false positives, and recall as the ratio

of true positives to the sum of true positives and

false negatives.

To maximize the F1 score, we need to choose an

optimal threshold for binary classiﬁcation. Although

the ROC (Receiver Operating Characteristics) curve

11 gives us valuable insights into where this thresh-

old might occur, our method is more systematic.

By iterating over equally-spaced threshold values

from zero to one, computed an F1 score at each

gradation, we can choose the threshold which yields

the highest F1 score on average.

Fig. 11: Figure showing the ROC curve for all the points

in all the images. The threshold should be around the point

where the slope changes.

VI. RESULTS

A. Batch Prediction

As we have seen, window-wise prediction allows

us to use variation regularization as a de-noising

mechanism. We also leverage window-wise predic-

tion to perform prediction averaging, resulting in

empirically smoother, and more accurate output. In

order to compute multiple predictions for each pixel,

we use a stride of 24⇥12 for our 48⇥48 prediction

window. Consequently, we have 4 to 16 predictions

per pixel, depending on a pixel’s location within the

image slice. Figure 13 evinces the qualitative impact

of the overlapping-window prediction scheme.

B. Computational Performance

To evaluate the effect of window predictions on

computational speed, we computed predictions on

a Tesla C2070 GPU for various window sizes.

The predictions used non-overlapping windows for

Fig. 12: Figure illustrating window-wise prediction. Each

64 ⇥ 64 pixel input yields a 48 ⇥ 48 pixel output prediction.

Fig. 13: (Left) Predicted membranes without overlapping

windows. (Right) Predicted membranes with overlapping win-

dows of 48 ⇥ 48 and a stride of 24 ⇥ 12.

the sake of expediency. As shown in Figure 14,

the results demonstrate a signiﬁcant speedup with

increasing window sizes. For the largest window,

a speedup of ⇡ 140 times the prediction speed of

single-pixel output is achieved.

Fig. 14: Prediction speed vs output window sizes on Tesla

C2070 GPU.

Interestingly, the increasing window sizes did not

seem to impact predictive accuracy in a meaningful

way (see ﬁgure 15). The implication of this result is

that we can perform prediction without sacriﬁcing

accuracy.

C. Membrane Prediction

A sample output for membrane cell prediction

is shown in Figure 16. Although the results from

Fig. 15: Effect of output window size of 64 ⇥ 64 pixels

and 48 ⇥ 48 pixels on accuracy for membrane detection with

CNNs.

simulations with overlapping windows and TVR

look qualitatively better than simulations without

using these methods, no difference is seen for pixel-

wise accuracy for either membranes and synapses.

For this reason, we believe pixel-wise accuracy to

be a ﬂawed evaluation metric.

D. Synapse Prediction

An sample output for membrane prediction is

shown in Figure 17. Overall, our F1 score for

synapse prediction is 0.48. Bear in mind that our

predictions are on image slices of dimension 85⇥85

pixels rather than over the original 1024 ⇥ 1024

image. Examination of ﬁgure 17 reveals that our

prediction methodology can beneﬁt from a post-

processing step to ﬁlter out the noise in output

prediction.

Fig. 17: Labeled synapses (left) and predicted synapses

(right). Prediction is performed using an output window of

size of 48 ⇥ 48 and a stride length of 24 ⇥ 12.

E. Multi-dimensional Context Cues

We compare the performance of a classiﬁer using

two dimensional context against a classiﬁer using

three dimensional context from neighboring image

slices above and below the current slice. Figure

Fig. 16: Input image (left), labeled membranes (middle) and predicted membranes (right). Prediction is performed using an

output window of 48 ⇥ 48 and a stride of 24 ⇥ 12.

18 evinces three-dimensional context outperforms

classiﬁers which use two-dimensional context.

Fig. 18: Accuracy of synapse classiﬁcation with three-

dimensional context versus two-dimensional context

VII. CONCLUSION

We presented the design and architecture of a

convolutional neural network that utilizes batch

prediction methodologies to perform simultaneous

classiﬁcation of synapses and cell membranes. The

proposed method is at least 100 times faster com-

pared to the state-of-art pixel-wise prediction. We

achieve a F1-score of .48 for synapse detection.

Using batch prediction on output window sizes up

to 48 ⇥48, we claim no qualitative loss of accuracy,

nor loss of pixel-wise accuracy.

VIII. FUTURE WORK

Additional gains in efﬁciency can be gleaned

from simultaneous prediction of both synapse and

cell membrane class membership. We propose two

approaches for simultaneous prediction. First, we

can re-architect our network to add more neurons

in the logistic regression layer, affording us the

predictive power to classify both edges and synapses

using just one network. Alternatively, we can im-

plement a new convolutional network to extract

various neuronal features such as pre-synaptic and

post-synatptic clefts, and vesicles. Thereafter, we

would wire the output of our multi-feature network

to the input of a second network which outputs

simultaneous multi-class classiﬁcations.

ACKNOWLEDGMENT

The authors would like to thank Professor Pro-

topapas for his valuable feedback and our Teach-

ing Fellow, Thouis Ray Jones, for his mentorship

throughout the course of the project. We also ac-

knowledge the efforts of our project partner, Verena

Kaynig-Fittkau.

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APPENDIX

Algorithm 1 Algorithm for Adaptive Histogram

Equalization

for every pixel i (with grey level l) in image do

Initialize array Hist to zero

for every contextual pixel j do

Hist[g(j)] = Hist[g(j)] + 1

end for

Sum: CHist

k=0

Hist(k)

= CHist

⇤ L/W

end for

Algorithm 2 Sketch of the Watershed Algorithm

1) A set of markers, pixels where the ﬂooding

shall start, are chosen. Each is given a differ-

ent label.

2) The neighboring pixels of each marked area

are inserted into a priority queue with a pri-

ority level corresponding to the gray level of

the pixel.

3) The pixel with the highest priority level is

extracted from the priority queue. If the neigh-

bors of the extracted pixel that have already

been labeled all have the same label, then

the pixel is labeled with their label. All non-

marked neighbors that are not yet in the

priority queue are put into the priority queue.

4) Redo step 3 until the priority queue is empty.

Team

We are four students from Harvard SEAS

I am a Master's student in IACS. I did my undergrad at Columbia in Computer Science.

Hallvard Nydal

I am a student in SEAS from Norway. I used to be a professional cross-country skier.

Raphaël Pestourie

I'm a PhD student in Applied Physics. I have lost count of all the degrees I have. Also, I am French.

I'm Mina. I'm a Master's student in IACS, originally from Egypt. Fun fact: passport control mispelled my name when I was applying for a visa, so now I am legally registered in the US as Mena instead of Mina.

Fast Algorithms for Membrane and Synapse Detection

Team

Cole Diamond

Hallvard Nydal

Raphaël Pestourie

Mina Nassif

Full Paper

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