# The incredibly strange story of Einstein’s Nobel prize

Palash B. Pal
Department of Physics, University of Calcutta

(December 2021)

###### Abstract

It is well-known that Einstein got the 1921 Nobel prize not for his theory of
relativity, but for his theory of photoelectricity. It is not that well-known
that he did not get the prize in 1921. Why not, and when did he get it?

On 25th October 2021, I got a frenetic email. It was from an ex-student of
mine, who is now a professor at an undergraduate college. From the message, I
learned that she is also the Head of the Physics Deparment at the moment, and
she had sent the message in her capacity as the Head. After these bits of
information, the important part of the message was contained in the next
paragraph:

> We are planning to organize a Webinar on the occasion of “Centenary year of
> the Nobel Prize to Einstein”. … We want to arrange the webinar in the year
> 2021, date will be finalized according to your convenience.

To be sure, it is not clear how to detect freneticity in an email. When one
talks, the emotions come out through the pitch and the speed of the words
delivered. Written words have no representation of either of those qualities.
However, in this case, the signature was unmistakable. It was in the sentence
“We want to arrange the webinar in the year 2021”. Although it was not said
explicitly, it would not be unreasonable to guess that the reason for the
hurry is the occasion, as mentioned in the message itself: “Centenary year of
the Nobel Prize to Einstein”. Of course she was referring to the fact that
Einstein received the 1921 Nobel prize for Physics.

But there was no cause for hurry. It can be debated whether 2021 should be the
centenary year for the event of Einstein’s Nobel prize, or even whether there
was an event at all. In case you are wondering what I mean by that statement,
let me say, without beating around the bush, that although Einstein got the
1921 Nobel Prize for Physics, he did not get in 1921.

Nobel Prize for Physics is usually announced in October. The preparation for
the choice starts the year before that. In other words, for the 2015 Nobel
Prize, say, the first step was taken in September 2014. At that time, letters
and messages were sent by a five- or six-member Nobel Committee to a lot of
luminaries, asking for their suggestions for the next year’s prize. The
deadline for submitting suggestions is the end of the month of January, of the
year of the award. A few months then go by while the Committee deliberates,
and also consults with experts outside the Committee. In June or July, the
Committee prepares a report. It includes the names of the persons considered
for the prize, some account of the proceedings, and a recommendation for the
recipient(s) based on everything. This report is submitted to the Royal
Swedish Academy. The Academy makes the final decision. It may or may not
uphold the recommendation of the Committee. The would-be recipient is
announced in October, and the prize is awarded in a ceremony at the Royal
Swedish Academy held on the 10th of December.

From: https://www.nobelprize.org/nomination/physics/

Based on this timeline, one would conclude that Einstein, the recipient of the
1921 Nobel Prize for Physics, came to know about the decision in October 1921,
and received the prize in December of the same year. No, that did not happen
at all. But we must go back a few years before coming back to that part of the
story.

Some of Einstein’s phenomenal work appeared in 1905. That year, in fact, is
often called the “Annum mirabilis”, or the miracle year, for Einstein. He
submitted at least five papers in that year, all of which have become classic.
And, wonder of wonder, he did all the work at a time when he did not have an
academic position. He applied for quite a few positions earlier, and was
denied. Then, in 1902, he accepted a job as technical expert third class at
the patent office in Bern. During the Annum Mirabilis, he was still working
there.

I will not get into a history of how his work was received in the scientific
community. I will only mention that the recognition was not instantaneous.
Even in 1907, when he applied for a position at the University of Bern, his
application was rejected. He did not get an academic position until 1908, and
did not attend an academic conference until 1909. The position he obtained in
1908 was not a permanent one. His first permanent position was at the
University of Prague, where he moved in 1911. Then, in 1912, he was offered a
professorship at ETH Zürich, which he accepted and moved back to Switzerland.
Soon after, he was approached by people from Berlin, with the idea of a
membership at the Prussian Academy of Sciences. He accepted the position in
December 1913, and moved to Berlin on the 6th of April, 1914.

During all these turbulent years, his name started appearing in the Nobel
nominations. In fact, with the exceptions of the years 1911 and 1915, he was
nominated for the Nobel Physics prize every year from 1910 to 1922. In 1910,
there was just one person who proposed Einstein’s name. The person was Wilhelm
Ostwald, winner of the 1909 Chemistry Nobel, who, earlier in 1901, turned down
Einstein’s application for an assistantship in his research group. He was
joined by several others in 1912 and 1913, including some other Nobel
laureates. All these nominations were for his theory of Special Relativity.
Although some experimental confirmation of Einstein’s now-famous mass-energy
relation started appearing in 1908, even in 1913 it was argued that the
evidences were not compelling enough to merit a prize for the theory. Some
other confirmation of the theory appeared later, 1916 onward. But by then,
Einstein had published his General Theory of Relativity (GTR), and the tables
had turned. In fact, in 1916, he was nominated for his GTR, and also for his
work on Brownian motion which demonstrated the existence of molecules. There
was only one nomination in that year.

Let’s jump cut to 1921. By then, Einstein had become a household name. This is
not an exaggeration. Indeed his fame spread much beyond the circle of
physicists, even to lay people not directly involved with science, because of
the experiments performed by Arthur Eddington in 1919, which proved that the
path of light is bent by gravitation, in agreement with the prediction made in
Einstein’s GTR. In 1920, his nominations talked mainly about the GTR, as
expected.

For the 1921 prize, there was a strong note from Max Planck, who had won the
prize for 1918, nominating Einstein for GTR. It was a repeat of the request he
had made the earlier year. Carl Oseen, a theoretical physicist from the
University of Uppsala, proposed Einstein’s name for the photoelectric effect.
The committee requested its member Allvar Gullstrand to prepare a report on
the theory of relativity, and another member, Svante Arrhenius, a report of
the photoelectric effect. They were both celebrated sceintists. Gullstrand was
a professor of opthalmology who had worked on geometrical optics and won the
1911 prize for Physiology and Medicine for his contributions to the
functioning of the human eye. His report on relativity was highly critical of
the theory. He surmised that the effects of relativity would be unmeasurable,
“so small that in general they lie below the limits of experimental error”. On
the other side, Arrhenius, the 1903 Nobel laureate for Chemistry who is
sometimes called the “father of Physical Chemistry”, said that since Planck
had been awarded the Nobel for quantum theory as recently as in 1918, another
prize should not go in the same direction so soon. So, near the end of the
year 1921, the Nobel Prize committee decided that they could not find anyone
suitable for the prize for that year. The year of this writing, 2021, marks
the centenary of that decision.

In 1922, Einstein’s name was proposed again. Meanwhile, the campaign for him
had increased in strength. Maurice Brillouin (not the person who is
responsible for the idea of “Brillouin zone”) wrote, “Imagine for a moment
what the general opinion will be fifty years from now if the name Einstein
does not appear on the list of Nobel laureates.” Oseen repeated his nomination
for the photoelectric effect. Planck proposed to give the overdue 1921 prize
to Einstein and the 1922 prize to Niels Bohr. This was indeed possible,
because according to the Nobel Foundation’s statutes, when no acceptable
candidate can be found, the Nobel Prize can be reserved until the following
year.

The Committee again asked Gullstrand for a report on relativity, and
Gullstrand reiterated what he had written the year before. Oseen was asked as
well, to produce a report on photoelectric effect, and he gave an excellent
account of Einstein’s revolutionary contribution to its theory. The Committee
recommended Einstein for the 1921 prize, and Bohr for the 1922 prize, just as
Planck had suggested. The Swedish Academy upheld the decision. Accordingly, a
telegram was delivered to Einstein’s address in Berlin on the 10th of November
1922, informing him of the good news.

Now you might have started to think that the rest of the story would be
obvious: that Einstein went to Stockholm in the December of 1922 and received
his prize, the Nobel Physics prize for the year 1921. Wrong. That’s not what
had happened.

Einstein was not home when the telegram arrived. He and his wife Elsa were on
board a ship to Japan. He would not be back until March 1923\. So, obviously
he did not go to Stockholm to receive his prize in December 1922.

Certainly Einstein would not have looked at it as a lost opportunity. In fact,
during the last few years, he was really quite sure that he would receive the
Nobel Prize at some point. When he got divorced from his first wife Mileva
Marič in January 1919, he promised her that he would give her the entire Nobel
Prize money, whenever he would get it. So, clearly, the news of the Nobel
Prize did not come as a surprise to Einstein.

Indeed, in September of 1922, the 1914 Nobel Physics winner Max von Laue wrote
a letter to Einstein, telling him that it would be “desirable for you to be
present in Europe in December.” Laue knew about Einstein’s plan for visiting
Japan, and he advised Einstein not to go. Of course he did not mention the
Nobel Prize, but the hint was rather obvious. Einstein ignored Laue’s
suggestion. It may also be true that he wanted badly to get out of Germany at
that time. On 24th June 1922, Walter Rathenau, a politician and Einstein’s
friend, was assassinated. There were attempts at the lives of several other
people, which were clear signs of rising anti-semitism in Germany.

Anyway, the news must have reached Einstein during his journey. It is not
clear when that happened. There was no mention of the arrival of the news in
his diary.

It was clear, much before December, that Einstein would not be around to
accept his prize. The question then arose: who would receive it on his behalf?
Usually, when a recipient is absent for some reason, the person who represents
him or her at the ceremony is the Ambassador of the recipient’s native country
to Sweden, residing in Stockholm. So now a battle of sorts ensued: the bone of
contention being, what was Einstein’s native country?

Einstein was born in Germany in 1879 in the southern town of Ulm, so he must
have been a German citizen by birth. But he moved with his family: first to
Italy in 1894, and then to Switzerland in 1895. In 1896, he paid 3 marks to
obtain a document that proclaimed that he was not a German citizen anymore. He
remained stateless for the next five years, until he got the Swiss citizenship
in 1901. At the time when the Nobel prize was announced for him, he was
traveling with his Swiss passport. Clearly, then, it should have been the
Swiss Ambassador to Stockholm who should accept the prize for him!

But this is a story where nothing goes according to the expectation. The
information about Einstein’s passport was known to the German Foreign Office,
who passed it on to the German Ambassador in Sweden, Rudolph Nadolny. Nadolny
refused to believe it. He cannot be blamed for that. In 1922, Einstein was in
Berlin, a member of the Prussian Academy of Sciences. That position was
available only to German citizens. When Nadolny telegraphed to the Academy,
inquiring about the citizenship, the Academy replied what it knew and
believed: that Einstein was indeed a German. Nadolny showed the reply to the
Swiss Ambassador. He was surprised, probably unhappy, but he accepted the
situation. He thought that probably, since Einstein had been living in Berlin
for a while, he considered himself to be a German again. Nadolny graciously
stated that Einstein’s Swiss connection be duly mentioned in public statements
of any kind, and that the Swiss Ambassador be also invited to the ceremony and
to the banquet afterwards. In any case, it was Nadolny who accepted the prize
on behalf on Einstein in December 1922, and in the Nobel records he appeared
as a German.

The matter did not end there. The German Ministry of Science asked the Berlin
Academy to clear up the citizenship issue. The Academy sent its report on 23rd
January 1923. They said that, since the job at the Academy required a German
citizenship and Einstein had accepted the job, it could be concluded that he
was a German. Remember that Einstein was away in Japan when all these things
were going on. When he returned in March 1923, he was asked to give his view
on the matter. His letter, dated 24th March 1923, contained the following
lines:

> When my appointment to the Academy was being considered, my colleague Haber
> informed me that my appointment would result in my becoming a Prussian
> citizen. As I attached importance to retaining my nationality, I made
> acceptance of a possible appointment dependent on this, a stipulation which
> was agreed to.

It was clear that Einstein remained a Swiss citizen at heart. So, when it came
to the issue of handing over the Nobel prize to him, he preferred that it be
done by the Swiss Ambassador to Germany. In fact, on 6th April 1923,
Einstein’s stepdaughter Ilse wrote a letter to the Nobel Foundation, informing
that Professor Einstein would appreciate if the medal and diploma could be
sent to him in Berlin, and added that it is preferred that this is done
through diplomatic channels, and the “Swiss Embassy should be considered,
since Professor Einstein is a Swiss citizen.” Finally, the Swedish Ambassordor
to Germany, Baron Ramel, handed the prize over to Einstein in Berlin.

To summarize, if we were to celebrate the centenary of the Nobel prize
announcement or the formal presentation of the award, that would be in 2022\.
If we want to celebrate the centenary of Einstein actually receiving the
prize, that should happen in 2023.

There are a few things about the prize which have not been discussed yet.
First, what happened to the money? As I have already mentioned, Einstein
promised his first wife Mileva, at the time of their divorce in January 1919,
that she would receive the entire Nobel prize money. Einstein kept up to his
promise. Soon after he got the money, in 1923, he transferred the entire
amount to the bank account of Mileva. Mileva bought a house in Zürich. Albert
Einstein himself did not enjoy a penny of his Nobel prize.

The other pending thing is about the Nobel lecture. A Nobel prize winner is
supposed to give a Nobel lecture at the time when the prize is conferred, on
the work cited in the award. In Einstein’s case, the winner was absent at the
ceremony in December of 1922. After he came back to Europe in March 1923, he
received a letter from Svante Arrhenius, Director of the Nobel Institute and
an esteemed member of the Nobel Committee, requesting him to visit Sweden at a
time of his conveience, and telling him that he need not wait till the next
Nobel ceremony which would be held in December 1923. So Einstein organized a
trip to Sweden. On 11th July 1923, he gave a lecture: not in Stockholm in
front of the Royal Swedish Academy, but to the Nordic Assembly of Naturalists
at Göteborg. The audience consisted of about 2000 people, including the King
of Sweden. Because of the lack of anything better, this lecture is considered
to be his Nobel lecture ever since, not only unofficially but even by the
Nobel Prize Foundation, and can be obtained on their website, and printed in
authorized collections of Nobel Prize lectures.

But, unlike usual Nobel lectures, this was not a lecture of the work that was
cited in the award. The citation said that Einstein was receiving his prize
“for his services to Theoretical Physics, and especially for his discovery of
the law of the photoelectric effect.” There was no mention of relativity.
There are good reasons to believe that the subject was deliberately omitted,
since in his nomination history the reports on relativity were not favorable.
However, by an irony of fate, when Arrhenius invited him to Sweden, he left
the choice of the topic to the speaker, but added that something on his
relativity theory would be a good choice. So Einstein gave his Göteborg
lecture on “Fundamental ideas and problems of the theory of relativity”. There
was absolutely no reference to his own work on photoelectric effect: not even
once. The Nobel Foundation had to accept it as the overdue Nobel lecture. All
they could do is to add a comment: “The Lecture was not delivered on the
occasion of the Nobel Prize award, and did not, therefore, concern the
discovery of the photoelectric effect.” This comment appears as a footnote in
the Foundation’s website.

Was relativity totally overlooked in Einstein’s Nobel prize? Certainly the
prize was not given for relativity. Even if one accepts the argument, however
lame it might be, that there was not enough experimental evidence to support
the theory in 1921 or 1922, the Swedish Academy could have considered him for
a second Nobel for the Theory of relativity at some later time. They did not.
It is a pity that there was no member in the Committee who could evaluate
relativity at that time. The reports submitted on relativity were negative,
and certainly the prize could not be given on the basis of them. The Nobel
Committe probably began feeling that it would be an embarrassment if Einstein
hadn’t received the Nobel prize. So, to quote Einstein’s biographer Abraham
Pais, “Oseen’s proposal to give the award for photoelectricity must have come
as a relief of conflicting pressures.”

However, it has to be said that relativity was not completely omitted in the
entire event. The presentation speech for the 1921 Nobel Physics prize was
made by Svante Arrhenius. He started his speech like this:

> There is probably no physicist living today whose name has become so widely
> known as that of Albert Einstein. Most discussion centres on his theory of
> relativity. This pertains essentially to epistemology and has therefore been
> the subject of lively debate in philosophical circles. It will be no secret
> that the famous philosopher Bergson in Paris has challenged this theory,
> while other philosophers have acclaimed it wholeheartedly. The theory in
> question also has astrophysical implications which are being rigorously
> examined at the present time.

So, Arrhenius admired relativity and recognized its importance. But he thought
that it was essentially “epistemology”. The word, according to the Merriam-
Webster dictionary, means “the study or a theory of the nature and grounds of
knowledge especially with reference to its limits and validity”.

Maybe it was not possible to anticipate what role the theory would play in the
coming decades, in the discovery of new elementary particles, in the
understanding the behavior of heavy atoms, and in the birth and development of
the theory of the universe as a whole. But from the presentation speech, it
seems that the people in Nobel Foundation did not even realize that relativity
was a theory of Physics. They brought up Bergson’s philosophical arguments in
the context. Einstein liked and respected Bergson as a person. About his
philosophy, he apparently commented, “Gott verzeih ihm” (God forgive him).

Was Einstein hurt, for no mention of relativity, then or ever again, in the
circle of Nobel awards? Probably he did not care. The fame came to him anyway.
The money did not come to him. As for the prize itself, or in general about
prizes, he was probably not a big enthusiast. A few incidents might throw
light on his attitude.

The Planck medal is the highest award of the German Physical Society. It was
instituted in 1929, and Einstein was the recipient of the inaugural year. The
day of the award, he did some work in the morning and went to the house of his
doctor friend, Janos Plesch, for lunch. After lunch, he fell asleep on a
couch. He got up at four. The ceremony was supposed to begin at five. Suddenly
he realized that he might be asked to speak at the occasion. So he sat down at
Plesch’s table, and grabbed the nearest piece of paper, which happened to be a
bootmaker’s bill. He scribbled on it for twenty minutes. Half an hour later,
when Planck awarded the medal to him, he said, in his acceptance speech, that
he knew that he would be overwhelmed after receiving the prize and would be at
a loss for words, so he had written down his speech, and would read it out. He
pulled the shoe bill from his waistcoat pocket and started reading. After the
speech, Plesch told him that he needed the bill back. Einstein reached in his
pocket, pulled the bill and the medal that was wrapped in it, and gave the
whole thing to Plesch. Plesch wrote, “He never took it out, and never looked
at it again.”

In 1932, he was invited to become a member of a science academy. A form was
sent to him, to be filled out. It contained nine questions, including birth
details, education, publications and major scientific contributions. Einstein
completed the form the submitted it. There was no mention of his Nobel prize.
Certainly he considered it to be irrelevant to the answers of the questions
asked.

Probably there is nothing to be surprised about, at least in the light of the
other things that we summarized here. It is said that truth is stranger than
fiction. Certainly the entire story appears almost unreal, or maybe magic-
real. That is why I could not help using a Marquezian title to this article,
mimicking “The incredible and sad tale of innocent Erendira and her cruel
grandmother”.

## Material obtained from:

  * [1] Abraham Pais, “Subtle is the Lord” (1982).
  * [2] Banesh Hoffmann, “Albert Einstein creator and rebel” (1972).
  * [3] Ronald W. Clark, “Einstein: the life and times” (1971).
  * [4] https://www.nobelprize.org/
  * [5] Barbara Wolff, https://www.einstein-website.de/z_information/nobelpreisgeld.html
  * [6] Gautam Gangopadhyay, https://gautamgangopadhyay.blogspot.com/2021/11/blog-post_19.html
  * [7] Palash Baran Pal, “Einstein-er uttoradhikar” (2011).


11institutetext: Michigan State University, East Lansing, MI 48824, USA
11email<EMAIL_ADDRESS>11email<EMAIL_ADDRESS>
# Iris-SAM: Iris Segmentation Using a Foundational Model

Parisa Farmanifard 11 Arun Ross 11

###### Abstract

Iris segmentation is a critical component of an iris biometric system and it
involves extracting the annular iris region from an ocular image. In this
work, we develop a pixel-level iris segmentation model from a foundational
model, viz., Segment Anything Model (SAM), that has been successfully used for
segmenting arbitrary objects. The primary contribution of this work lies in
the integration of different loss functions during the fine-tuning of SAM on
ocular images. In particular, the importance of Focal Loss is borne out in the
fine-tuning process since it strategically addresses the class imbalance
problem (i.e., iris versus non-iris pixels). Experiments on ND-IRIS-0405,
CASIA-Iris-Interval-v3, and IIT-Delhi-Iris datasets convey the efficacy of the
trained model for the task of iris segmentation. For instance, on the ND-
IRIS-0405 dataset, an average segmentation accuracy of 99.58% was achieved,
compared to the best baseline performance of 89.75%.

###### Keywords:

Iris Segmentation Biometrics Segment Anything Model

##  1 Introduction

The human iris is a highly intricate structure whose distinctive patterns form
the basis of one of the most secure forms of biometric recognition [7, 13].
The structure of the iris includes the pupillary zone immediately surrounding
the pupil, the ciliary zone comprising the rest of the iris, and the
collarette forming a boundary between the two zones. The iris also features
contraction furrows, which are circular folds created by the contraction of
the pupillary muscles, and crypts, which are small openings or depressions in
the iris tissue (fig. 1) [14].

Figure 1: Iris anatomy in the near-infrared spectrum.

The process of accurately delineating the iris from the surrounding structures
(sclera, pupil, eyelids, eyelashes) is termed iris segmentation [22]. A well-
segmented iris results in more reliable feature extraction, which, in turn,
enhances the accuracy of recognition systems. Several iris segmentation
methods have been developed, ranging from the simple Integro-Differential
Operator [8] to those based on complex convolutional neural networks [15].
However, iris segmentation has its own challenges. Variability in
illumination, occlusions from eyelashes or eyelids, reflections, and low
resolution in distant captures are among the issues complicating the process
[4] and can substantially affect the segmentation quality. Additionally,
intrinsic challenges such as the dynamic nature of the iris, aging effects,
and diseases can further complicate the segmentation task. Within this
challenging context, the recent surge in the capabilities of foundation neural
network models offers a promising path. The advent of foundational models has
revolutionized various domains of research and application. These models,
characterized by their vast size, extensive training data, and remarkable
generalization abilities, have set new benchmarks in tasks ranging from
natural language processing to image recognition [5, 11]. In the realm of
image segmentation, foundational models have played a pivotal role.
Traditional segmentation methods have evolved significantly with the
integration of deep learning techniques. Fully Convolutional Network (FCN)
[20] and U-Net [25] have laid the groundwork for advanced segmentation tasks.
These models have been instrumental in achieving state-of-the-art performance
in various segmentation challenges, demonstrating the power of deep learning
in extracting meaningful patterns from complex visual data.
Among the recent advancements in segmentation models, the Segment Anything
Model (SAM) by Meta stands out as a versatile and powerful tool. SAM’s
architecture, designed to handle a wide range of segmentation tasks,
represents a significant leap in the field [17]. Its ability to segment
diverse objects in complex scenes has shown great promise in extending the
boundaries of what segmentation models can achieve. However, applying
foundational models like SAM to specific domains, such as iris segmentation,
presents unique challenges. The complexity of iris patterns, variations in
lighting, occlusions due to eyelashes, varying pupil sizes, the pose of the
iris with respect to the camera, the acquisition of the image in the near-
infrared spectrum, etc., are significant hurdles in achieving high-precision
segmentation [7]. The transfer of knowledge from general segmentation tasks to
such a specialized domain requires careful fine-tuning and adaptation of the
model. Approaches like transfer learning, where a model trained on a large
dataset is fine-tuned on a smaller, domain-specific dataset, have proven
effective [24].
The central inquiry of this study thus emerges: how effective are these
foundational models, particularly the Segment Anything Model (SAM), when
applied to the task of iris segmentation? By exploring this question, in this
paper, we delve into the challenge of iris segmentation, a crucial component
for iris recognition, and investigate how foundation models can be fine-tuned
and augmented with specific loss functions [19] to achieve enhanced
performance.

##  2 Background

###  2.1 Foundational Models

One of the most popular foundational models, OpenAI’s GPT-3, was trained on
diverse internet text. This vast training allows it to write essays, answer
questions, and even generate code with minimal task-specific prompts [5].
Google’s BERT uses bi-directional training on vast text corpora to capture
intricate language relationships, setting new performance benchmarks across
numerous NLP tasks [9]. In the visual domain, Vision Transformers (ViT)
tessellate images into fixed-size patches, linearly embed them, and process
them through transformer layers [10].

While foundation models emerged with a strong emphasis on NLP tasks, their
underlying architecture and learning mechanisms have found relevance in
computer vision. The ability of these models to capture hierarchical features
and understand contexts makes them suitable for visual tasks, where often,
object representations and spatial relationships dictate the outcome. For
instance, Vision Transformers (ViT) have demonstrated how techniques
originally designed for sequence data (like text) can be repurposed for image
data, leading to impressive results in image classification [10]. The success
of such models suggests potential utility in more intricate tasks like
segmentation, where both global and local contexts matter.

###  2.2 SAM

The Segment Anything Model (SAM) [17] exemplifies the adaptability of
foundation models in complex computer vision tasks like segmentation. Its
architecture includes an image encoder creating high-dimensional embeddings, a
prompt encoder for interpreting user inputs (like bounding boxes) into
features, and a mask decoder that merges these to predict segmentations. SAM’s
vision encoder, a key component, processes images to generate detailed feature
maps, crucial for capturing contextual, localizing, and pattern-recognition
information across large image areas. The mask decoder then translates these
features into precise pixel-level decisions for segmentation, using up-
sampling layers to refine the output. SAM’s ability to acquire a broad
knowledge base from varied training scenarios enables it to adapt to new
segmentation tasks with minimal additional training, bridging foundational
model capabilities with the specific needs of segmentation accuracy.

###  2.3 Iris Segmentation

Over the years, iris segmentation methods have evolved from traditional image
processing techniques to sophisticated machine learning algorithms. The
seminal work of Daugman utilized integro-differential operators to detect the
iris’ circular patterns by maximizing contour sharpness. This approach,
however, has its limitations with non-circular and partially occluded irides.
Subsequent advances have introduced active contour models [26, 1], which
iteratively evolve a curve under constraints in order to fit non-circular and
non-elliptical boundries. These models, while more flexible than their
predecessors, require careful initialization and can be computationally
intensive. OSIRIS [23] is an open-source software for iris recognition, using
Hough transform and Gabor filters for accurate iris segmentation. It serves as
a benchmark in evaluating new iris segmentation techniques. SegNet [3] is
another well-known segmentation method that emerged as a notable deep learning
architecture. Originally developed for scene understanding, SegNet’s efficient
encoder-decoder structure makes it well-suited for iris segmentation tasks. It
effectively captures contextual information and detailed spatial resolution,
crucial for accurately delineating the iris from other ocular components. The
U-Net architecture, a variant of CNNs, has gained traction for its efficacy in
segmenting medical images, including the iris [18], by using a contracting
path to capture context and a symmetrically expanding path that enables
precise localization [25].

##  3 Proposed Method

In this work, the SAM technique, renowned for its adaptability in medical
image segmentation [21], has been fine-tuned for the specific task of iris
segmentation. In the context of iris segmentation, the bounding box prompt
emerges as the most effective, providing clear demarcation of the Region of
Interest (ROI) with minimal user input. This approach is not only intuitive
but also aligns with standard ophthalmic measurement practices, ensuring both
accuracy and efficiency [21]. In the context of iris segmentation using SAM,
bounding boxes are crucial for directing the model’s focus to the relevant
region (the iris) in each image. These bounding boxes are derived from ground
truth masks during training using a specialized function that calculates the
minimum and maximum coordinates encompassing the iris, with random adjustments
in perturbed bounding boxes that entail unpredictably altering their size and
position. This randomness enhances a model’s flexibility and generalization to
new data. This approach ensures that the model consistently focuses on the
iris region across different images.

In iris segmentation, one often encounters a significant class imbalance. That
is, the number of pixels belonging to the target object (iris pixels) might be
much smaller compared to the background (non-iris pixels). Traditional loss
functions, such as Cross-Entropy or Mean Squared Error, when used in such
scenarios, tend to get overwhelmed by the sheer number of negative samples
(non-iris pixels), leading the model to produce trivial solutions that
identify everything as the background (fig. 5).

Focal Loss, introduced by Lin et al. [19], provides a refined approach to
handle the prevalent issue of class imbalance. Rather than treating all
misclassified samples uniformly, the Focal Loss assigns varying weights to
samples based on their misclassification levels (gives more weight to samples
that the model struggles to identify as either part of the iris or non-iris,
and less weight to samples that the model finds easy to categorize as
belonging to the iris or non-iris regions). This is done to focus the model’s
learning more on challenging cases. Focal Loss is derived from standard cross-
entropy loss [6] that struggles to address this imbalance, predominantly
focusing on the majority class and, thus, overlooking the minority class,
i.e., the iris pixels in our case.

Below, we see the cross-entropy loss for binary classification. For a given
probability $p$ of the positive class (iris) and the ground truth label $y$,
the CE loss is defined as [19]:

$CE(p,y)=\begin{cases}-\log(p),&\text{if }y=1\\\
-\log(1-p),&\text{otherwise.}\end{cases}$ (1)

For a pixel $p_{i}$, the cross-entropy loss is given by:

$L_{CE}(p_{i})=-y_{i}\log(\hat{y}_{i})-(1-y_{i})\log(1-\hat{y}_{i}),$ (2)

where, $y_{i}$ is the ground truth (1 for iris, 0 for background) and
$\hat{y}_{i}$ is the predicted probability for the pixel being part of the
iris. However, in such scenarios with a large class imbalance, the CE loss can
be overwhelmed by a great number of easy-to-classify negative samples (non-
iris pixels). As a result, we need to have balancing and focusing factors to
solve the issue.

Focal Loss is introduced to down-weight the correctly classified pixels, thus
forcing the model to focus on hard-to-classify pixels. To address the
limitations of cross-entropy loss in the presence of class imbalance, Focal
Loss, denoted as $FL(p_{t})$, is introduced. It is formulated as:

$FL(p_{t})=-(1-p_{t})^{\gamma}\log(p_{t}).$ (3)

$p_{t}$ is the model’s estimated probability for the class with label $y=1$.
$\alpha$ is a weighting factor to balance the importance of positive vs.
negative examples and $\gamma$ is the focusing parameter, adjusting the rate
at which easy examples are down-weighted. For our problem, we adapt it as
follows:

If the ground truth label $y=1$ (iris), then $p_{t}=\hat{y}_{i}$; otherwise
$p_{t}=1-\hat{y}_{i}$. The modified Focal Loss for a pixel $p_{i}$ becomes:

$L_{\text{Focal}}(p_{i})=-\alpha(1-p_{t})^{\gamma}y_{i}\log(p_{t})-(1-\alpha)p_{t}^{\gamma}(1-y_{i})\log(1-p_{t}).$
(4)

Focal Loss, with its modulating factor $(1-p_{t})^{\gamma}$ diminishes the
contribution of well-classified (easy) pixels and amplifies the loss for
misclassified ones, especially near the iris boundary. Here, $\alpha$ is a
balancing factor, and $\gamma$ is the focusing parameter that determines how
much the weight of well-classified examples should be reduced. As $\gamma$
increases, the effect of the modulating factor becomes more pronounced. The
intuition behind Focal Loss can be visualized in the iris segmentation task.
In an eye image, vast areas are not part of the iris (sclera, pupil, eyelids,
etc.). When using standard cross-entropy, the model quickly learns to predict
these easy, non-iris regions correctly, while struggling with the actual iris
region due to class imbalance. The function comprises two parts:

  * •

The first part, $-\alpha(1-p_{t})^{\gamma}y_{i}\log(p_{t})$, focuses on the
positive class. The modulating factor $(1-p_{t})^{\gamma}$ increases the loss
for misclassified or uncertain positive examples.

  * •

The second part, $-(1-\alpha)p_{t}^{\gamma}(1-y_{i})\log(1-p_{t})$, focuses on
the negative class. The modulating factor $p_{t}^{\gamma}$ increases the loss
for misclassified or overconfident negative examples.

Figure 2: Proposed network (Iris-SAM) using Segment Anything Model (SAM) [17].
(a) Training and (b) Inference/Testing.

By adjusting $\alpha$ and $\gamma$, Focal Loss can be fine-tuned for different
datasets and imbalance problems, aiming to improve the performance on hard
examples. During the training phase, we utilize a dataset consisting of iris
images $I_{1},I_{2},\ldots,I_{n}$, each paired with a specific bounding box
$B_{1},B_{2},\ldots,B_{n}$ and a corresponding ground truth mask
$M_{1},M_{2},\ldots,M_{n}$. The model, when presented with an image $I_{j}$,
produces a predicted mask $O_{j}$. A key objective is to enhance the agreement
between $O_{j}$ and the ground truth mask $M_{j}$, with the Intersection over
Union (IoU) metric serving as the measure of this congruence. The IoU is
defined as $\text{IoU}(O_{j},M_{j})=\frac{|O_{j}\cap M_{j}|}{|O_{j}\cup
M_{j}|}$, indicating the extent of overlap between the predicted and actual
iris regions (the standard deviation of IoU across all images is also
computed, offering insight into the consistency of the model’s performance).
Crucially, the difference between the predicted mask $O_{j}$ and the ground
truth mask $M_{j}$ plays a pivotal role in the training process. This
disparity indicates how much the model’s predictions deviate from the real
iris area, forming a basis for calculating the weights used in the Focal Loss
function. These weights, derived from the degree of misalignment between
$O_{j}$ and $M_{j}$, are employed to adjust the model’s learning focus,
particularly directing attention toward more challenging segmentation areas.
In Focal Loss, the weights for each example are dynamically calculated using
the formula $\alpha\times(1-p_{t})^{\gamma}$, where $p_{t}$ is derived from
the model’s output. The model’s output logits are first transformed into a
probability $p$ using the sigmoid function. Then, $p_{t}$ is determined based
on the ground truth label $y$: if $y=1$, $p_{t}=p$; if $y=0$, $p_{t}=1-p$.
This approach ensures that the loss focuses more on challenging examples where
the model is less confident. This adjustment is vital for refining the
accuracy of the model’s mask decoder, as it guides the model to learn more
effectively from areas where its predictions are less accurate, thereby
enhancing its overall segmentation capability.

SAM’s versatile architecture allows for the generation of multiple masks
corresponding to various objects or regions within an image. However, to
tailor its capability to our specific need of segmenting a single object (the
iris), we utilize the multimask_output parameter within the model’s prediction
method. The parameter is a boolean flag that guides the model’s output
behavior. As can be seen in fig. 2, setting multimask_output to False
instructs SAM to deviate from its default behavior of identifying multiple
objects. Instead, it concentrates on generating a singular focused mask
output. This output, in the context of our work, is the segmented iris region.
This focused approach of generating a single mask output ensures that the
model’s computational resources and learning capacity are entirely devoted to
the task of iris segmentation. It negates the diversion of attention to
multiple regions, thereby enhancing the precision and accuracy of the
segmentation process. This modification is pivotal for the specific
requirements of iris biometric systems, where the delineation precision of the
iris region directly impacts the system’s reliability and performance.

The data split information for the experiments can be seen in table 1.
Datasets are captured using diverse camera systems and under varying
environmental conditions, resulting in a wide range of image qualities, iris
textures, and lighting variations. In our experiments, the SGD optimizer with
a learning rate of 0.0001 and training for 100 epochs was optimal, achieving
convergence without overfitting. This configuration not only optimized the
learning curve but also stabilized the loss across epochs, as seen in the
accompanying plots (fig. 4).

##  4 Experimental Results

###  4.1 Dice, Triplet, and Focal Losses

In our iris segmentation experiments, Focal Loss outperformed Dice and Triplet
losses, excelling in managing class imbalance by focusing on difficult
examples, as shown in our training loss graph (fig. 3(a)). This approach
effectively emphasized critical iris details and boundaries, leading to more
accurate segmentation. Focal Loss achieved lower, stable loss values rapidly,
indicating efficient learning. Conversely, Dice Loss showed higher,
fluctuating loss values, struggling with false positives and false negatives,
while Triplet Loss, proved ineffective for segmentation, lacking in pixel-wise
accuracy.

Table 1: Dataset information.

Dataset | Total | Train | Test
---|---|---|---
| (Images/Identities) | (Images/Identities) | (Images/Identities)
CASIA-Iris-Interval-v3 | 2655/249 | 2294/199 | 361/50
ND-Iris-0405 | 804/346 | 624/276 | 180/70
IIT-Delhi-Iris | 2240/224 | 1790/179 | 450/45

(a)

(b)

Figure 3: (a) Training loss over 100 epochs for Dice, Triplet, and Focal Loss
functions on the Casia-Iris-Interval-v3 dataset. Focal Loss converges rapidly
to a lower value, indicating efficient learning, while Dice and Triplet losses
exhibit higher variability and slower convergence. (b) Precision-Recall curve
of our method on different test datasets when the Focal Loss was used during
training.

###  4.2 Segmentation Results

Our experimentation spanned across various settings of the focusing parameter,
$\gamma$, within the Focal Loss, examining its impact on the model’s
performance. We tested $\gamma$ values of 1, 2, and 5 on the CASIA-Iris-
Interval-v3 dataset (fig. 4(a)), aiming to calibrate the loss function’s
sensitivity to misclassified instances. A $\gamma$ value of 2 emerged as the
optimal choice, striking a delicate balance between learning efficiency and
robustness (fig. 4(b)). While a higher $\gamma$ of 5 initially seemed
promising, it ultimately led to overfitting–a testament to the nuanced trade-
offs in model training. The overfitting was evidenced by a good performance on
the training set that did not generalize well to unseen data.

As can be seen in table 2, a $\gamma$ value of 2, achieved a high Average IoU
of 96.94% on the CASIA-Iris-Interval-v3 and 99.58% on the ND-Iris-0405
dataset, demonstrating its effectiveness in iris segmentation. However,
performance slightly dipped on the IIT-Delhi-Iris dataset with an Average IoU
of 94.34%, indicating a nuanced variance in efficacy across different
datasets. This marginal drop in performance can be attributed to the dataset’s
unique characteristics, particularly, the prevalence of dense eyelashes. The
eyelashes present a complex segmentation challenge. Our model’s nuanced
attempt to delineate these eyelashes more accurately contributed to the slight
reduction in the overall IoU score. It is a reflection of the model’s
sensitivity to fine-grained features, a trait that is both a strength and a
point of careful consideration in dataset diversity. The good performance of
our model is further underscored by the standard deviation associated with the
Average IoU scores, which is between 0.002 to 0.008 across the evaluated
datasets. The limited variance in the IoU scores suggests a high level of
consistency and reliability in the model’s ability to segment iris regions,
despite the inherent challenges presented by different images. Such
consistency is particularly noteworthy when considering the complexity of iris
textures and the potential for occlusions like eyelashes and reflections,
which typically introduce variability in segmentation tasks.

(a)

(b)

Figure 4: (a) FineTuning + Focal Loss (Iris-SAM) using the default pre-trained
model "ViT_h" with different $\gamma$ values on CASIA-Iris-Interval-v3
dataset. (b) FineTuning + Focal Loss (Iris-SAM) using the default pre-trained
model "ViT_h" on three different datasets.

The baseline section of table 2 reports the performance of established iris
segmentation models that are used as benchmarks. The OSIRIS model provides a
baseline with an average IoU of 86.28% (±6.50), while the DRN and Context-100k
models show improved performance and consistency, with IoUs around 89% and
lower standard deviations. SegNet achieves an IoU of 89.75% but with slightly
higher variability. The numerical performance of the baseline methods further
conveys the efficacy of the proposed method which has significantly higher IoU
scores and near-zero standard deviation underscoring its advanced segmentation
accuracy and consistency across various datasets. In figs. 6, 7 and 8 we
demonstrate the effectiveness of incorporating Focal Loss into our fine-tuning
process for the Segment Anything Model (SAM). The bounding box is denoted in
green and the pixels classified as iris are marked in blue. Prior to the
integration of Focal Loss, the SAM’s performance, while adequate, fell short
of achieving the high levels of accuracy needed for precise iris segmentation
(fig. 5). The initial fine-tuning phase was unable to consistently
differentiate the intricate iris patterns from surrounding ocular structures.
However, the adaptation of Focal Loss marked a significant turning point in
our experiments and allowed the SAM to focus more on discerning the nuanced
boundaries of the iris. The post-Focal Loss fine-tuning results, as showcased
in the figures, reveal a substantial alignment with the ground-truth data. The
contrast between the pre and post-Focal Loss output is a testament to the loss
function’s impact. Where the original fine-tuning failed to capture certain
iris details, the model augmented with Focal Loss succeeded in delineating the
iris with remarkable precision. These results not only validate the rationale
behind using the Focal Loss but also underscore its potential in handling
diversity of pixels in both the positive and negative classes.

As depicted in fig. 10 and fig. 11, our fine-tuned SAM model, with Focal Loss,
exhibited an uncanny ability to not only match but sometimes surpass the
ground-truth masks in accuracy. This was particularly evident when the model
adeptly filled in missing iris segments and refrained from misclassifying
eyelashes as iris tissue. To further validate our results, we plotted
precision and recall curves for the three datasets (fig. 3(b)), which reveal
the model’s strong segmentation capability, with ND-Iris-0405 showing near-
perfect precision. While CASIA-Iris-Interval-v3 and IIT-Delhi-Iris experience
minor precision declines at full recall, the consistently high performance
indicates effective feature capture for iris segmentation.

Table 2: Iris segmentation accuracy in terms of Average IoU% $\pm$ STD. Our method is observed to perform much better than the four baseline techniques. Further, it exhibits good generalization capability. Our Method | Dataset | Accuracy
---|---|---
Iris-SAM | CASIA-Iris-Interval-v3 | 96.94 $\pm$ 0.005
Iris-SAM | ND-Iris-0405 | 99.58 $\pm$ 0.003
Iris-SAM | IIT-Delhi-Iris | 94.34 $\pm$ 0.008
Our Method’s Generalization
Train | Test | Accuracy
ND-Iris-0405 | IIT-Delhi-Iris | 93.75 $\pm$ 0.016
ND-Iris-0405 | CASIA-Iris-Interval-v3 | 95.26 $\pm$ 0.009
CASIA-Iris-Interval-v3 | IIT-Delhi-Iris | 93.86 $\pm$ 0.010
CASIA-Iris-Interval-v3 | ND-Iris-0405 | 98.86 $\pm$ 0.002
IIT-Delhi-Iris | ND-Iris-0405 | 98.92 $\pm$ 0.002
IIT-Delhi-Iris | CASIA-Iris-Interval-v3 | 95.49 $\pm$ 0.008
Baselines [16]
Method | Dataset | Accuracy
OSIRIS | ND-Iris-0405 | 86.28 $\pm$ 6.50
DRN | ND-Iris-0405 | 89.61 $\pm$ 5.08
Context-100k | ND-Iris-0405 | 89.45 $\pm$ 3.85
SegNet | ND-Iris-0405 | 89.75 $\pm$ 4.95

(a) FT Only - S1002R10

(b) FT Only - S1019R04

(c) FT Only - S1053L05

Figure 5: FineTuning (FT) sample results (CASIA-Iris-Interval-v3).

(a) FT+Focal - S1002R10

(b) FT+Focal - S1019R04

(c) FT+Focal - S1053L05

Figure 6: FT + Focal Loss (Iris-SAM) sample results (CASIA-Iris-Interval-v3).

(a) FT+Focal - 04267d227

(b) FT+Focal - 04350d458

(c) FT+Focal - 04370d361

Figure 7: FT + Focal Loss (Iris-SAM) sample results (ND-IRIS-0405).

(a) FT+Focal - 008_07

(b) FT+Focal - 015_04

(c) FT+Focal - 075_06

Figure 8: FT + Focal Loss (Iris-SAM) sample results (IIT-Delhi-Iris).

###  4.3 Cross-Dataset Model Generalization

The generalization capability of our method was further put to the test by
training on ND-Iris-0405 and evaluating on the IIT-Delhi-Iris, and CASIA-Iris-
Interval-v3 datasets resulting in a commendable generalization score of
93.75%, and 95.26%, respectively. For training, we utilized our fine-tuned
model already trained on each dataset. This cross-dataset validation
underscores our model’s adaptability and its potential for deployment in
varied scenarios (more generalization results are shown in table 2).

(a) Identity 011_01

(b) Identity 013_06

Figure 9: Generalization results using ND-Iris-0405 (train) and IIT-Delhi-Iris
(test). (a) Is an example of failure segmentation. (b) An interesting
observation of the model trying to segment the eyelashes even for completely
new dataset.

##  5 Is SAM More Accurate Than GT?

A notable observation from our experiments, as illustrated in fig. 10 and fig.
11, is the occasional superiority of the model-predicted masks over the
ground-truth masks.

(a) Identity S1019L04

(b) Identity S1009R05

Figure 10: Examples where the predicted mask appears to be more accurate than
the ground truth mask in the CASIA-Iris-Interval-v3 dataset.

(a) Identity 032_07

(b) Identity 019_05

Figure 11: Examples where the predicted mask appears to be more accurate than
the ground truth mask in the IIT-Delhi-Iris dataset.

Figure 12: Evaluation of our model on a challenging dataset (irides with
glasses) without further tuning. As can be seen, the results vary, with some
instances showing good outcomes and others less favorable.

In fig. 10, marked by a red arrow, we observe an instance where the ground-
truth mask partially omits a segment of the iris. In contrast, the model’s
prediction captures this missing section, demonstrating a nuanced
understanding of the iris structure. This instance is especially interesting
considering the model achieved this higher accuracy with a relatively
straightforward fine-tuning process. It suggests that the model, guided by the
Focal Loss, has developed a nuanced perception of iris features, surpassing
even the manually annotated ground truth in certain aspects. fig. 11 presents
a scenario where the ground-truth mask inaccurately depicts eyelashes as part
of the iris. However, the model’s predicted mask displays an interesting
discernment by correctly excluding the eyelashes from the iris segmentation.
This precision highlights the model’s capability to distinguish between
closely situated but distinct features within the ocular region, a crucial
requirement for reliable iris segmentation. Firstly, the model’s refined
handling of ground-truth annotations showcases its deep understanding of iris
morphology. Secondly, its precise discrimination between the iris and adjacent
elements underscores the model’s accuracy, which is essential for the
reliability of iris biometric systems.

##  6 Conclusion and Future Work

In our study, the enhanced SAM model with Focal Loss has significantly
advanced iris segmentation, achieving Average IoU scores of 96.94% and 99.58%
on CASIA-Iris-Interval-v3 and ND-Iris-0405 datasets, respectively, and
maintaining consistent performance with a very low standard deviation.
Notably, the model handled complex scenarios, including dense eyelashes, as
evidenced by its performance on the IIT-Delhi-Iris dataset, though it
highlighted areas for future refinement. This work sets a new benchmark for
iris segmentation and paves the way for exploration of other challenges in
iris segmentation, such as the processing of off-axis irides and images
acquired in other spectral bands besides NIR.

Acknowledgement. We thank the University of Salzburg and Halmstad University
for providing the ground truth datasets [2, 12]. The code supporting the
findings of this study is available upon request.

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