assignment 11.1 image labeling

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Biology Teaching Resources

Label the Eye

This worksheet shows an image of the eye with structures numbered. Students practice labeling the eye or teachers can print this to use as an assessment.

There are two versions on the google doc and pdf file, one where the word bank is included and another with no word bank for differentiation. You could also print both and students could practice with the word bank first and then try without.

The image was modified from an eye diagram at Wikimedia Commons . I added the numbers and additional errors to identify structures that weren’t on the original diagram.

You can also download this version of the same activity where students drag and drop labels to an image. The images are on google slides, which makes it easy to assign on Google Classroom.

There are a few terms that can be vague, for example, the aqueous humor could also be labeled as the aqueous chamber. Zonule of Zinn can also be called suspensory ligaments.

You could also have the students list the general functions of each of the structures shown as part of their assignment.

Shannan Muskopf

Human Anatomy & Physiology: A&P Chapter 11 Fundamentals of the Nervous System and Nervous Tissue Flashcards

Drag the appropriate labels to their respective targets.

What structural classification describes the neuron associated with the neuroglia shown by E and F?

Destruction of which of the neuroglial cell types leads to the disease multiple sclerosis (MS)?

Which lettered region in the figure is referred to as the soma ?

Where do most action potentials originate?

Initial segment

What opens first in response to a threshold stimulus?

Voltage-gated Na + channels

What characterizes depolarization, the first phase of the action potential?

The membrane potential changes from a negative value to a positive value.

What characterizes repolarization, the second phase of the action potential?

Once the membrane depolarizes to a peak value of +30 mV, it repolarizes to its negative resting value of -70 mV.

What event triggers the generation of an action potential?

The membrane potential must depolarize from the resting voltage of -70 mV to a threshold value of -55 mV.

What is the first change to occur in response to a threshold stimulus?

Voltage-gated Na + channels change shape, and their activation gates open.

What type of conduction takes place in unmyelinated axons?

Continuous conduction

An action potential is self-regenerating because __________.

depolarizing currents established by the influx of Na + ‎ flow down the axon and trigger an action potential at the next segment

Why does regeneration of the action potential occur in one direction, rather than in two directions?

The inactivation gates of voltage-gated Na + ‎ channels close in the node, or segment, that has just fired an action potential.

What is the function of the myelin sheath?

The myelin sheath increases the speed of action potential conduction from the initial segment to the axon terminals.

What changes occur to voltage-gated Na + and K + channels at the peak of depolarization?

Inactivation gates of voltage-gated Na + ‎ channels close, while activation gates of voltage-gated K + ‎ channels open.

In which type of axon will velocity of action potential conduction be the fastest?

Myelinated axons with the largest diameter

Ions are unequally distributed across the plasma membrane of all cells. This ion distribution creates an electrical potential difference across the membrane. What is the name given to this potential difference?

Resting membrane potential (RMP)

Sodium and potassium ions can diffuse across the plasma membranes of all cells because of the presence of what type of channel?

Leak channels

On average, the resting membrane potential is -70 mV. What does the sign and magnitude of this value tell you?

The inside surface of the plasma membrane is much more negatively charged than the outside surface.

The plasma membrane is much more permeable to K + than to Na + . Why?

There are many more K + leak channels than Na + leak channels in the plasma membrane.

The resting membrane potential depends on two factors that influence the magnitude and direction of Na + and K + diffusion across the plasma membrane. Identify these two factors.

The presence of concentration gradients and leak channels

What prevents the Na + and K + gradients from dissipating?

Na + -K + ATPase

Which of the following describes the nervous system integrative function?

analyzes sensory information, stores information, makes decisions

Which of the following types of glial cells monitors the health of neurons, and can transform into a special type of macrophage to protect endangered neurons?

Which of the following are bundles of neurofilaments that are important in maintaining the shape and integrity of neurons?

neurofibrils

Which of the following is true of axons?

A neuron can have only one axon, but the axon may have occasional branches along its length.

Which of the following is NOT a functional classification of neurons?

Which of the following is NOT true of association neurons?

Most association neurons are confined within the peripheral nervous system (PNS).

Neurons are also called nerve cells.

Unmyelinated fibers conduct impulses faster than myelinated fibers.

At which point of the illustrated action potential are the most gated Na + channels open?

In myelinated axons the voltage-regulated sodium channels are concentrated at the nodes of Ranvier.

Collections of nerve cell bodies in the peripheral nervous system are called ________.

What does the central nervous system use to determine the strength of a stimulus?

frequency of action potentials

Which of the neuroglial cell types shown form myelin sheaths within the CNS?

Which of the neuroglial cell types shown is the most abundant in the CNS?

Saltatory conduction is made possible by ________.

the myelin sheath

Large-diameter nerve fibers conduct impulses much faster than small-diameter fibers.

The part of a neuron that conducts impulses away from its cell body is called a(n) ________.

Schwann cells are functionally similar to ________.

oligodendrocytes

Bipolar neurons are commonly ________.

found in the retina of the eye

If bacteria invaded the CNS tissue, microglia would migrate to the area to engulf and destroy them.

Myelination of the nerve fibers in the central nervous system is the job of the oligodendrocyte.

What structural classification describes this neuron?

What part of the nervous system performs information processing and integration?

central nervous system

Which of the following types of neurons carry impulses away from the central nervous system (CNS)?

Efferent nerve fibers may be described as motor nerve fibers.

The period after an initial stimulus when a neuron is not sensitive to another stimulus is the ________.

absolute refractory period

Which of the following is NOT a type of circuit?

pre-discharge circuits

Which part of the neuron is responsible for generating a nerve impulse?

What are ciliated CNS neuroglia that play an active role in moving the cerebrospinal fluid called?

ependymal cells

Which of the following is NOT one of the basic functions of the nervous system?

regulation of neurogenesis

The oligodendrocytes can myelinate several axons.

Immediately after an action potential has peaked, which cellular gates open?

What type of stimulus is required for an action potential to be generated?

a threshold level depolarization

Which of the following is not a function of the autonomic nervous system?

innervation of skeletal muscle

A neuron that has as its primary function the job of connecting other neurons is called a(n) ________.

association neuron

Which of the following is a factor that determines the rate of impulse propagation, or conduction velocity, along an axon?

degree of myelination of the axon

Neurons in the CNS are organized into functional groups.

Which of the following peripheral nervous system (PNS) neuroglia form the myelin sheaths around larger nerve fibers in the PNS?

Schwann cells

Neuroglia that control the chemical environment around neurons by buffering ions such as potassium and recapturing and recycling neurotransmitters are ________.

The action potential is caused by permeability changes in the plasma membrane.

Which of the choices below describes the ANS?

motor fibers that conduct nerve impulses from the CNS to smooth muscle, cardiac muscle, and glands

Which of the following is not characteristic of neurons?

They are mitotic.

Which ion channel opens in response to a change in membrane potential and participates in the generation and conduction of action potentials?

voltage-gated channel

Which of the following circuit types is involved in the control of rhythmic activities such as the sleep-wake cycle, breathing, and certain motor activities (such as arm swinging when walking)?

reverberating circuits

The __________ is due to the difference in K + and Na + concentrations on either side of the plasma membrane, and the difference in permeability of the membrane to these ions.

resting membrane potential

During depolarization, the inside of the neuron's membrane becomes less negative.

The all-or-none phenomenon as applied to nerve conduction states that the whole nerve cell must be stimulated for conduction to take place.

Image Labeling by Assignment

• Published: 12 January 2017
• Volume 58 , pages 211–238, ( 2017 )

Cite this article

• Freddie Åström 1 ,
• Stefania Petra 2 ,
• Bernhard Schmitzer 3 &
• Christoph Schnörr   ORCID: orcid.org/0000-0002-8999-2338 4  

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45 Citations

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We introduce a novel geometric approach to the image labeling problem. Abstracting from specific labeling applications, a general objective function is defined on a manifold of stochastic matrices, whose elements assign prior data that are given in any metric space, to observed image measurements. The corresponding Riemannian gradient flow entails a set of replicator equations, one for each data point, that are spatially coupled by geometric averaging on the manifold. Starting from uniform assignments at the barycenter as natural initialization, the flow terminates at some global maximum, each of which corresponds to an image labeling that uniquely assigns the prior data. Our geometric variational approach constitutes a smooth non-convex inner approximation of the general image labeling problem, implemented with sparse interior-point numerics in terms of parallel multiplicative updates that converge efficiently.

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For locations i close to the boundary of the image domain where patch supports \({\mathscr {N}}_{p}(i)\) shrink, the definition of the vector \(w^{p}\) has to be adapted accordingly.

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Acknowledgements

Support by the German Research Foundation (DFG) was gratefully acknowledged, Grant GRK 1653.

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Heidelberg Collaboratory for Image Processing, Heidelberg University, Heidelberg, Germany

Freddie Åström

Mathematical Imaging Group, Heidelberg University, Heidelberg, Germany

Stefania Petra

CEREMADE, University Paris-Dauphine, Paris, France

Bernhard Schmitzer

Image and Pattern Analysis Group, Heidelberg University, Heidelberg, Germany

Christoph Schnörr

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Correspondence to Christoph Schnörr .

Appendix 1: Basic Notation

For \(n \in {\mathbb {N}}\) , we set \([n] = \{1,2,\ldots ,n\}\) . \({\mathbbm {1}}= (1,1,\ldots ,1)^{\top }\) denotes the vector with all components equal to 1, whose dimension can either be inferred from the context or is indicated by a subscript, e.g.,  \({\mathbbm {1}}_{n}\) . Vectors \(v^{1}, v^{2},\ldots \) are indexed by lowercase letters and superscripts, whereas subscripts \(v_{i},\, i \in [n]\) , index vector components. \(e^{1},\ldots ,e^{n}\) denotes the canonical orthonormal basis of \(\mathbb {R}^{n}\) .

We assume data to be indexed by a graph \({\mathscr {G}}=({\mathscr {V}},{\mathscr {E}})\) with nodes \(i \in {\mathscr {V}}=[m]\) and associated locations \(x^{i} \in \mathbb {R}^{d}\) , and with edges \({\mathscr {E}}\) . A regular grid graph and \(d=2\) is the canonical example. But \({\mathscr {G}}\) may also be irregular due to some preprocessing like forming super-pixels, for instance, or correspond to 3D images or videos ( \(d=3\) ). For simplicity, we call i location although this actually is \(x^{i}\) .

If \(A \in \mathbb {R}^{m \times n}\) , then the row and column vectors are denoted by \(A_{i} \in \mathbb {R}^{n},\, i \in [m]\) and \(A^{j} \in \mathbb {R}^{m},\, j \in [n]\) , respectively, and the entries by \(A_{ij}\) . This notation of row vectors \(A_{i}\) is the only exception from our rule of indexing vectors stated above.

The componentwise application of functions \(f :\mathbb {R}\rightarrow \mathbb {R}\) to a vector is simply denoted by f ( v ), e.g., 

Likewise, binary relations between vectors apply componentwise, e.g., \(u \ge v \;\Leftrightarrow \; u_{i} \ge v_{i},\; i \in [n]\) , and binary componentwise operations are simply written in terms of the vectors. For example,

where the latter operation is only applied to strictly positive vectors \(q > 0\) . The support \({{\mathrm{supp}}}(p) = \{p_{i} \ne 0 :i \in {{\mathrm{supp}}}(p)\} \subset [n]\) of a vector \(p \in \mathbb {R}^{n}\) is the index set of all non-nonvanishing components of p .

\(\langle x, y \rangle \) denotes the standard Euclidean inner product and \(\Vert x\Vert = \langle x, x \rangle ^{1/2}\) the corresponding norm. Other \(\ell _{p}\) -norms, \(1 \le p \ne 2 \le \infty \) , are indicated by a corresponding subscript, \( \Vert x\Vert _{p} = \big (\sum _{i \in [d]} |x_{i}|^{p}\big )^{1/p}, \) except for the case \(\Vert x\Vert = \Vert x\Vert _{2}\) . For matrices \(A, B \in \mathbb {R}^{m \times n}\) , the canonical inner product is \( \langle A, B \rangle = \hbox {tr}(A^{\top } B) \) with the corresponding Frobenius norm \(\Vert A\Vert = \langle A, A \rangle ^{1/2}\) . \({{\mathrm{Diag}}}(v) \in \mathbb {R}^{n \times n},\, v \in \mathbb {R}^{n}\) , is the diagonal matrix with the vector v on its diagonal.

Other basic sets and their notation are

the positive orthant

the set of strictly positive vectors

the ball of radius r centered at p

the unit sphere

the probability simplex

and its relative interior

closure (not regarded as manifold)

the sphere with radius 2

the assignment manifold

and its closure (not regarded as manifold)

For a discrete distribution \(p \in \varDelta _{n-1}\) and a finite set \(S=\{s^{1},\ldots ,s^{n}\}\) vectors, we denote by

the mean of S with respect to p .

Let \({\mathscr {M}}\) be a any differentiable manifold. Then \(T_{p}{\mathscr {M}}\) denotes the tangent space at base point \(p \in {\mathscr {M}}\) and \(T{\mathscr {M}}\) the total space of the tangent bundle of \({\mathscr {M}}\) . If \(F :{\mathscr {M}} \rightarrow {\mathscr {N}}\) is a smooth mapping between differentiable manifold \({\mathscr {M}}\) and \({\mathscr {N}}\) , then the differential of F at \(p \in {\mathscr {M}}\) is denoted by

If \(F :\mathbb {R}^{m} \rightarrow \mathbb {R}^{n}\) , then \(DF(p) \in \mathbb {R}^{n \times m}\) is the Jacobian matrix at p , and the application DF ( p )[ v ] to a vector \(v \in \mathbb {R}^{m}\) means matrix-vector multiplication. We then also write DF ( p ) v . If \(F = F(p,q)\) , then \(D_{p}F(p,q)\) and \(D_{q}F(p,q)\) are the Jacobians of the functions \(F(\cdot ,q)\) and \(F(p,\cdot )\) , respectively.

The gradient of a differentiable function \(f :\mathbb {R}^{n} \rightarrow \mathbb {R}\) is denoted by \(\nabla f(x) = \big (\partial _{1} f(x),\ldots ,\partial _{n} f(x)\big )^{\top }\) , whereas the Riemannian gradient of a function \(f :{\mathscr {M}} \rightarrow \mathbb {R}\) defined on Riemannian manifold \({\mathscr {M}}\) is denoted by \(\nabla _{{\mathscr {M}}} f\) . Eq. ( 2.5 ) recalls the formal definition.

The exponential mapping [ 21 , Def. 1.4.3]

maps the tangent vector v to the point \(\gamma _{v}(1) \in {\mathscr {M}}\) , uniquely defined by the geodesic curve \(\gamma _{v}(t)\) emanating at p in direction v . \(\gamma _{v}(t)\) is the shortest path on \({\mathscr {M}}\) between the points \(p, q \in {\mathscr {M}}\) that \(\gamma _{v}\) connects. This minimal length equals the Riemannian distance \(d_{{\mathscr {M}}}(p,q)\) induced by the Riemannian metric , denoted by

i.e., the inner product on the tangent spaces \(T_{p}{\mathscr {M}},\,p \in {\mathscr {M}}\) , that smoothly varies with p . Existence and uniqueness of geodesics will not be an issue for the manifolds \({\mathscr {M}}\) considered in this paper.

The exponential mapping \({{\mathrm{Exp}}}_{p}\) should not be confused with

the exponential function \(e^{v}\) used, e.g., in ( 6.1 );

the mapping \(\exp _{p} :T_{p}{\mathscr {S}} \rightarrow {\mathscr {S}}\) defined by Eq. ( 3.8a ).

The abbreviations “l.h.s.” and “r.h.s.” mean left-hand side and right-hand side of some equation, respectively. We abbreviate with respect to by “wrt.”

Appendix 2: Proofs and Further Details

1.1 proofs of section 2.

(of Lemma 1 ) Let \(p \in {\mathscr {S}}\) and \(v \in T_{p}{\mathscr {S}}\) . We have

and \(\big \langle \psi (p), D\psi (p)[v] \big \rangle = \langle 2 \sqrt{p}, \frac{v}{\sqrt{p}} \rangle = 2 \langle {\mathbbm {1}}, v \rangle = 0\) , that is, \(D\psi (p)[v] \in T_{\psi (p)}{\mathscr {N}}\) . Furthermore,

i.e., the Riemannian metric is preserved and hence also the length L ( s ) of curves \(s(t) \in {\mathscr {N}},\, t \in [a,b]\) : Put \(\gamma (t) = \psi ^{-1}\big (s(t)\big ) = \frac{1}{4} s^{2}(t) \in {\mathscr {S}},\, t \in [a,b]\) . Then \(\dot{\gamma }(t)=\frac{1}{2} s(t) \dot{s}(t) = \frac{1}{2} \psi \big (\gamma (t)\big ) \dot{s}(t) = \sqrt{\gamma (t)} \dot{s}(t)\) and

\(\square \)

(of Prop.  1 ) Setting \(g:{\mathscr {N}} \rightarrow \mathbb {R}\) , \(q \mapsto g(s) := f\big (\psi ^{-1}(s)\big )\) with \(s = \psi (p) = 2 \sqrt{p}\) from ( 2.3 ), we have

because the 2-sphere \({\mathscr {N}}=2{\mathbb {S}}^{n-1}\) is an embedded submanifold, and hence the Riemannian gradient equals the orthogonal projection of the Euclidean gradient onto the tangent space. Pulling back the vector field \(\nabla _{{\mathscr {N}}} g\) by \(\psi \) using

we get with ( 7.1 ), ( 7.4 ) and \(\Vert s\Vert =2\) and hence \(s/\Vert s\Vert = \frac{1}{2} \psi (p)=\sqrt{p}\)

which equals ( 2.6 ). We finally check that \(\nabla f_{{\mathscr {S}}}(p)\) satisfies ( 2.5 ) (with \({\mathscr {S}}\) in place of \({\mathscr {M}}\) ). Using ( 2.1 ), we have

(of Prop.  2 ) The geodesic on the 2-sphere emanating at \(s(0) \in {\mathscr {N}}\) in direction \(w=\dot{s}(0) \in T_{s(0)}{\mathscr {N}}\) is given by

Setting \(s(0)=\psi (p)\) and \(w = D\psi (p)[v]=v/\sqrt{p}\) , the geodesic emanating at \(p=\gamma _{v}(0)\) in direction v is given by \(\psi ^{-1}\big (s(t)\big )\) due to Lemma 1 , which results in ( 2.7a ) after elementary computations. \(\square \)

1.2 Proofs of Section 3 and Further Details

(of Prop.  3 ) We have \(p = \exp _{p}(0)\) and

which confirms ( 3.10 ), is equal to ( 3.9 ) at \(t=0\) and hence yields the first expression of ( 3.11 ). The second expression of ( 3.11 ) follows from a Taylor expansion of ( 2.7a )

(of Lemma 4 ) By construction, \(S(W) \in {\mathscr {W}}\) , that is, \(S_{i}(W) \in {\mathscr {S}},\; i \in [m]\) . Consequently,

The upper bound corresponds to matrices \(\overline{W}^{*} \in \overline{{\mathscr {W}}}\) and \(S(\overline{W}^{*})\) where for each \(i \in [m]\) , both \(\overline{W}^{*}_{i}\) and \(S_{i}(\overline{W}^{*})\) equal the same unit vector \(e^{k_{i}}\) for some \(k_{i} \in [m]\) . \(\square \)

(Explicit form of ( 3.27 )) The matrices \(T^{ij}(W) = \frac{\partial }{\partial W_{ij}} S(W)\) are implicitly given through the optimality condition ( 2.9 ) that each vector \(S_{k}(W),\, k \in [m]\) , defined by ( 3.13 ) has to satisfy

while temporarily dropping below W as argument to simplify the notation, and using the indicator function \(\delta _{{\mathrm {P}}} = 1\) if the predicate \({\mathrm {P}}={\mathrm {true}}\) and \(\delta _{{\mathrm {P}}} = 0\) otherwise, we differentiate the optimality condition on the r.h.s. of (7.12),

Since the vectors \(\phi (S_{k},L_{r})\) given by ( 7.13 ) are the negative Riemannian gradients of the (locally) strictly convex objectives ( 2.8 ) defining the means \(S_{k}\) [ 21 , Thm. 4.6.1], the regularity of the matrices \(H^{k}(W)\) follows. Thus, using ( 7.14f ) and defining the matrices

results in ( 3.27 ). The explicit form of this expression results from computing and inserting into ( 7.14f ) the corresponding Jacobians \(D_{p}\phi (p,q)\) and \(D_{q}\phi (p,q)\) of

The term ( 7.16b ) results from mapping back the corresponding vector from the 2-sphere \({\mathscr {N}}\) ,

where \(\psi \) is the sphere map ( 2.3 ) and \(d_{{\mathscr {N}}}\) is the geodesic distance on \({\mathscr {N}}\) . The term ( 7.16c ) results from directly evaluating ( 3.12 ). \(\square \)

(of Lemma 5 ) We first compute \(\exp _{p}^{-1}\) . Suppose

Thus, in view of ( 3.9 ), we approximate

Applying this to the point set \({\mathscr {P}}\) , i.e., setting

step (3) of ( 3.31 ) yields

Finally, approximating step (4) of ( 3.31 ) results in view of Prop.  3 in the update of p

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Åström, F., Petra, S., Schmitzer, B. et al. Image Labeling by Assignment. J Math Imaging Vis 58 , 211–238 (2017). https://doi.org/10.1007/s10851-016-0702-4

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Received : 25 March 2016

Accepted : 30 December 2016

Published : 12 January 2017

Issue Date : June 2017

DOI : https://doi.org/10.1007/s10851-016-0702-4

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• Image labeling
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