Lecture 8 - Fingerprint Analysis
Lecture 8翻译技巧(词义的延伸)
英语中，特别在现代英语中，常常用一个表示具体形象 的词来表示一种属性、一个事物或一种概念。翻译这类 词时，一般可将其词义作抽象化的引伸，译文才能流畅、 自然。 将表示具体形象的词译成该形象所代表的属性的词 There is a mixture of the tiger and the ape in the character of the imperialists. 帝国主义者的性格既残暴，又狡猾。 这里把tiger（老虎）和ape（猿）这两个具体形象引伸 为这两个形象所代表的属性：“残暴”和“狡猾”。 Every life has its roses and thorns. 每个人的生活都有甜和苦。 这里把roses（玫瑰）和thorns（刺）这两个具体形象 引伸为这两个形象所代表的属性：“甜”和“苦”。
On Studies 王佐良译《论读书》 水天同《论学问》 Studies serve for delight, for ornament, and for ability. 水译：读书为学的用途是娱乐、装饰和增长才识。 王译：读书足以怡情，足以傅彩，足以长才。 Their chief use for delight, is in privateness and retiring; for ornament, is in discourse; and for ability, is in the judgment, and disposition of business. 水译：在娱乐上学问的主要的用处是幽居养静；在装饰 上学问的用处是辞令；在长才上学问的用处是对于事务 的判断和处理。 王译：其怡情也，最见于独处幽居之时；其傅彩也，最 见于高谈阔论之中；其长才也，最见于处世判事之际。
细胞生物学课件英文版-基因和染色体分析
PCR is used in forensic analysis
VNTRs: Variable Number Tandem Repeats
STRs: short tandem repeats •4 to 40 repeats in various positions (loci)
“DNA fingerprint”
– Conserves energy
• Don’t make what you don’t need!
• Multicellular
– Allows specialization of cell types
– Allows growth and development
• How do we know that
Fig 10-23, 10-24
How can we change DNA information?
Make site specific changes
Transform into a strain that has no
DNA repair
Fig 10-34
Reporter Genes
Fig 10-29
organism • Mechanisms to determine the sequence of DNA • Ways to alter and change DNA sequences • Ways to put DNA back into organisms
• And if we can do all that: use stem cells to alter/repair damage
• What are some of the specialized proteins produced in these cell types?
FingerPrint
Type of fingerprint
Fingerprint Feature Extraction and Numeric Meta-base Creation
1. Fingerprint Image Pre-processing The main steps involved in the pre-processing include: (a) enhancement (b) binarization (c) segmentation, (d) thinning. 2. Fingerprint Feature Extraction and Numeric Meta-base Creation
FingerPrint
History of using fingerprint as identification
1. Antiquity and the medieval period
Fingerprints have been found on ancient Babylonian clay tablets, seals, and pottery. They have also been found on the walls of Egyptian tombs and on Minoan, Greek, and Chinese pottery, as well as on bricks and tiles from ancient Babylon and Rome. Some of these fingerprints were deposited unintentionally by the potters and masons as a natural consequence of their work, and others were made in the process of adding decoration. However, on some pottery, fingerprints have been impressed so deeply into the clay that they were possibly intended to serve as an identifying mark by the maker.
近五年高考英语重点单词清单
近五年高考英语重点单词清单1. Analyze - to examine something in detail, typically for the purpose of explanation or interpretation.Example: The teacher asked the students to analyze the poem and identify its main themes.2. Evaluate - to assess or judge the value, importance, or quality of something.Example: The committee will evaluate the candidates based on their skills and experience.3. Synthesize - to combine different ideas, information, or elements to form a coherent whole.Example: In his research paper, he synthesized various theories to support his argument.4. Interpret - to explain the meaning of something, especially in relation toa particular situation or set of circumstances.Example: The lawyer interpreted the new law for his clients and advised them on how it might affect their case.5. Comprehend - to understand the meaning or significance of something. Example: It is essential for students to comprehend the text before attempting to answer the questions.6. Infer - to deduce or conclude something from evidence or reasoning rather than from explicit statements.Example: Based on the clues in the story, the detective was able to infer who the murderer was.7. Context - the circumstances or conditions in which something exists or occurs.Example: It is important to consider the context when interpreting ahistorical document.8. Convey - to communicate or express a thought, feeling, or idea.Example: The artist used colors and brushstrokes to convey a sense of joy and energy in her painting.9. Illustrate - to provide examples, explanations, or visual representations to make something clearer or more understandable.Example: The professor used diagrams and charts to illustrate his lecture on complex mathematical concepts.10. Critique - a detailed analysis or evaluation of something, such as a work of art, literature, or music.Example: The art critic wrote a scathing critique of the new exhibition, highlighting its lack of originality.11. Hypothesize - to propose an explanation or theory based on limited evidence, with the intention of further investigation.Example: The scientist hypothesized that the new drug would have a positive effect on patients with the disease.12. Contradict - to assert the opposite or deny something that has been stated or believed.Example: The witness's testimony contradicted the defendant's alibi and weakened their case.13. Advocate - to publicly support or recommend a particular cause, policy, or idea.Example: The environmentalist advocated for stricter regulations to protect endangered species.14. Revise - to alter or make changes to something, especially in order to improve it.Example: The student had to revise his essay several times before he was satisfied with the final draft.15. Collaborate - to work together with others on a project or task. Example: The group members collaborated to complete the presentation on time.16. Analytical - characterized by a systematic and logical approach to problem-solving or decision-making.Example: The job requires strong analytical skills to analyze data andidentify trends.17. Proponent - a person who advocates or supports a particular idea, cause, or policy.Example: The senator is a proponent of tax reform and has introduced severalbills on the subject.18. Ambiguous - open to more than one interpretation or having double meaning. Example: The ambiguous statement from the politician left the reporters confused about his stance on the issue.19. Cite - to refer to a source or quote as evidence or support for an argument or claim.Example: The author cited numerous studies to back up her claims in the research paper.20. Elaborate - to explain or give greater detail on a particular point or idea.Example: The speaker asked the panelists to elaborate on their views during the Q&A session.21. Justify - to provide reasons or evidence to support or explain a decision, action, or belief.Example: The defendant's lawyer had to justify why his client should be granted bail.22. Paraphrase - to restate something in different words, often to clarify meaning or simplify complex ideas.Example: The student was asked to paraphrase the poem in his own words.23. Resemble - to have a similar appearance, character, or quality to someone or something else.Example: The two brothers strongly resemble each other, often causing confusion among their classmates.24. Contrary - opposite in nature, direction, or meaning.Example: Contrary to popular belief, not all cats hate water; some actually enjoy swimming.25. Evaluate - to assess or judge the value, importance, or quality of something.Example: The committee will evaluate the candidates based on their skills and experience.26. Interpret - to explain the meaning of something, especially in relation toa particular situation or set of circumstances.Example: The lawyer interpreted the new law for his clients and advised them on how it might affect their case.27. Comprehend - to understand the meaning or significance of something. Example: It is essential for students to comprehend the text before attempting to answer the questions.28. Infer - to deduce or conclude something from evidence or reasoning rather than from explicit statements.Example: Based on the clues in the story, the detective was able to infer who the murderer was.29. Context - the circumstances or conditions in which something exists or occurs.Example: It is important to consider the context when interpreting ahistorical document.30. Convey - to communicate or express a thought, feeling, or idea.Example: The artist used colors and brushstrokes to convey a sense of joy and energy in her painting.31. Illustrate - to provide examples, explanations, or visual representations to make something clearer or more understandable.Example: The professor used diagrams and charts to illustrate his lecture on complex mathematical concepts.32. Critique - a detailed analysis or evaluation of something, such as a work of art, literature, or music.Example: The art critic wrote a scathing critique of the new exhibition, highlighting its lack of originality.33. Hypothesize - to propose an explanation or theory based on limited evidence, with the intention of further investigation.Example: The scientist hypothesized that the new drug would have a positive effect on patients with the disease.34. Contradict - to assert the opposite or deny something that has been stated or believed.Example: The witness's testimony contradicted the defendant's alibi and weakened their case.35. Advocate - to publicly support or recommend a particular cause, policy, or idea.Example: The environmentalist advocated for stricter regulations to protect endangered species.36. Revise - to alter or make changes to something, especially in order to improve it.Example: The student had to revise his essay several times before he was satisfied with the final draft.37. Collaborate - to work together with others on a project or task. Example: The group members collaborated to complete the presentation on time.38. Analytical - characterized by a systematic and logical approach to problem-solving or decision-making.Example: The job requires strong analytical skills to analyze data andidentify trends.39. Proponent - a person who advocates or supports a particular idea, cause, or policy.Example: The senator is a proponent of tax reform and has introduced several bills on the subject.40. Ambiguous - open to more than one interpretation or having double meaning. Example: The ambiguous statement from the politician left the reporters confused about his stance on the issue.41. Cite - to refer to a source or quote as evidence or support for an argument or claim.Example: The author cited numerous studies to back up her claims in the research paper.42. Elaborate - to explain or give greater detail on a particular point or idea.Example: The speaker asked the panelists to elaborate on their views during the Q&A session.43. Justify - to provide reasons or evidence to support or explain a decision, action, or belief.Example: The defendant's lawyer had to justify why his client should be granted bail.44. Paraphrase - to restate something in different words, often to clarify meaning or simplify complex ideas.Example: The student was asked to paraphrase the poem in his own words.45. Resemble - to have a similar appearance, character, or quality to someone or something else.Example: The two brothers strongly resemble each other, often causing confusion among their classmates.46. Contrary - opposite in nature, direction, or meaning.Example: Contrary to popular belief, not all cats hate water; some actually enjoy swimming.47. Anticipate - to expect or foresee something happening in the future. Example: The weather forecast anticipated heavy rain and thunderstorms for the weekend.48. Distinguish - to recognize or perceive the difference between two or more things.Example: The detective used fingerprint analysis to distinguish the suspect from the other individuals at the crime scene.49. Emphasize - to give special importance or prominence to something. Example: The teacher emphasized the need for students to study regularly for the upcoming exam.50. Evoke - to bring a feeling, memory, or image into the mind.Example: The photograph evoked strong emotions of nostalgia and longing.51. Persuade - to convince someone to do something or believe in something through reasoning or argumentation.Example: The speaker used compelling evidence to persuade the audience to support his proposal.52. Reflect - to think deeply or carefully about something, often resulting ina change of behavior or attitude.Example: After the incident, he reflected on his actions and realized he needed to apologize.53. Simulate - to imitate or recreate the conditions or appearance ofsomething for the purpose of study or training.Example: The flight simulator allowed pilots to simulate various flying situations without leaving the ground.54. Symbolize - to represent or stand for something else, often an abstract concept or idea.Example: The dove is often used to symbolize peace and harmony.55. Validate - to confirm or establish the truth, accuracy, or validity of something.Example: The experiment was conducted multiple times to validate the results.56. Clarify - to make something clearer or easier to understand by explaining or providing additional information.Example: The teacher clarified the assignment instructions to avoid any confusion.57. Elaborate - to provide more detail or develop further on a particular point or idea.Example: The writer was asked to elaborate on his argument in the next draft of the paper.58. Examine - to inspect, investigate, or evaluate something in detail. Example: The doctor examined the patient's symptoms to determine a diagnosis.59. Predict - to forecast or estimate what will happen in the future based on current evidence or knowledge.Example: The weather forecast predicted heavy snowfall for the next week.60. Reinforce - to strengthen or support something, often by providing additional evidence or examples.Example: The coach reinforced the importance of practice in order to improve performance.61. Suggest - to propose or recommend something as a possible course of action or solution.Example: The report suggested several strategies for reducing traffic congestion in the city.62. Contrast - to compare two or more things, highlighting their differences. Example: The essay contrasted the economic policies of two differentpresidents.63. Establish - to set up or create something, usually with the intention ofit being long-lasting or recognized.Example: The company was established in 1985 and has since become a leader in the industry.64. Identify - to recognize, discover, or establish the identity or nature of something or someone.Example: The detective worked tirelessly to identify the murderer from the available evidence.65. Recall - to remember or bring back into the mind.Example: She struggled to recall the details of the conversation she had with the client earlier that day.66. Validate - to confirm or establish the truth, accuracy, or validity of something.Example: The experiment was conducted multiple times to validate the results.67. Verify - to confirm or prove the truth, accuracy, or validity of something. Example: The administrator verified the student's identification before allowing them to enter the building.68. Corroborate - to confirm or support something by providing additional evidence or testimony.Example: Multiple witnesses corroborated the victim's account of the incident.69. Deduce - to reach a conclusion or inference based on evidence, reasoning, or information.Example: The detective carefully analyzed the clues and deduced who theculprit was.70. Dispute - to argue or debate the truth or validity of something.Example: The two scholars disputed the interpretation of the historical document.71. Exemplify - to serve as a typical or representative example of something. Example: The author used the character of Atticus Finch to exemplify moral integrity.72. Perceive - to become aware of or understand something through the senses or intuition.Example: The artist wanted the audience to perceive the painting as a reflection of their own emotions.73. Resolve - to find a solution or come to a decision about something. Example: The negotiators worked together to resolve the conflict peacefully.74. Advocate - to publicly support or recommend a particular cause, policy, or idea.Example: The activist strongly advocated for equal rights and social justice.75. Attribute - to regard something as being caused by a particular person, thing, or circumstance.Example: The success of the project was attributed to the hard work and dedication of the team.76. Compensate - to make up for something, often by providing an equivalent benefit or advantage.Example: The travel expenses were compensated by the company for the employees attending the conference.77. Endorse - to publicly support or approve of someone or something. Example: The celebrity endorsed the new brand of sports shoes in a television commercial.78. Facilitate - to make an action or process easier or smoother.Example: Technology has facilitated communication and collaboration among people around the world.79. Implement - to put a plan, decision, or agreement into effect or action. Example: The government implemented new policies to address the issue of climate change.80. Institute - to establish or set in motion something, such as a system, organization, or rule.Example: The university instituted new guidelines for student conduct on campus.81. Justify - to provide reasons or evidence to support or explain a decision, action, or belief.Example: The defendant's lawyer had to justify why his client should be granted bail.82. Modify - to make partial or minor changes to something in order to improve or adapt it.Example: The designer modified the original dress design based on the client's feedback.。
fingerprints
1. INTRODUCTION
Compact fingerprint sensors can now be easily integrated into devices such as laptops, cellular phones, PDAs, etc. The limited platen size of these sensors results in the acquisition of flat/dab prints that contain reduced information (e.g., fewer minutiae points) compared to rolled fingerprints1, 2 as seen in Figure 1. Thus, multiple impressions of the same finger may have only a small region of overlap, thereby degrading the matching performance of the fingerprint authentication system. In order to address this problem, information from several impressions of a finger can be integrated to enhance the information content of the resulting fingerprint template. This process, known as mosaicing, is expected to improve the matching performance of a fingerprint system. Mosaicing can be accomplished at two distinct levels: (a) the image level (image mosaicing), where multiple impressions of a finger are combined together to generate an elaborate fingerprint - minutiae points are then extracted from the mosaiced fingerprint; and (b) the feature level (feature mosaicing), where the minutiae sets extracted from multiple impressions are combined to generate a composite feature set (Figure 2(a) and (b)). Both these schemes rely on a robust registration technique to accurately align a pair of impressions (or minutiae sets) before integrating them. One of the confounding factors in fingerprint registration is the presence of elastic deformation in constituent prints. The elastic deformation is a consequence of the elasticity of the skin and the non-uniform pressure applied by the finger on the platen of the sensor. This leads to a distortion of the ridges and the accompanying minutiae points. Thus, a simple affine transformation is not sufficient to register two such fingerprint impressions (or minutiae sets). The goal of this paper, in the context of mosaicing, is two-fold: 1. To incorporate a registration procedure that compensates for the non-linear distortion present between a pair of prints. 2. To compare the utility of a composite template generated by image mosaicing with that of feature mosaicing by examining their matching performance against a target set of prints.
答辩ppt-基于MATLAB的指纹识别概要
步骤六：将指纹样本特征模板录入指纹库
2.3 实验结果与分析
将指纹一样本和指纹一模板进行匹配 ，系统显示匹配成功，说明是同一个指纹
将指纹一样本和指纹四模板进行匹配 ，系统显示匹配失败，说明是不同的两个指纹 （更多实验结 果请看演示）
实验结果汇总与分析：
本实验共选取了4组指纹图像作为样本，4组随机指纹图像作为模板，共进行 了16次模拟匹配实验，其中4组匹配成功，12组匹配失败。16组实验中的实验结 果均与实际情况相同，所以本实验的识别率为100%。实验结果无误可靠。
3 指纹识别实验的创新性
1.1 指纹识别介绍
• 指纹识别：是目前生物检测学中研究最深入，应用最广 泛，发展最成熟的技术。指纹识别作为识别技术已经有 几个世纪的历史了。
• 指纹识别技术原理：通过分析指纹的全局特征和指纹的 局部特征，特征点如嵴、谷和终点、分叉点或分歧点， 从指纹中抽取的特征值可以非常的详尽，以便可靠地通 过指纹来确认一个人的身份。
步骤五：提取四张指纹图像的特征点 指纹识别系统的自动化水平,在很大程度上是依赖于系统提取的细节特征准确性。
对于细化后的二值图像都要计算每个点值其交叉数(Cn)。一点R的交叉数Cn 定义在一 个3×3的模板上，模板如图所示
R表示的是待检验的点，如果R表示的是端点，则它的8邻域点就满足：
如果M表示的是分叉点，则它的8邻域点就满足：
这种算法对每一个特征向量的要求很高，4维空间向量算法很复 杂，而且需要计算的工作量很大，而且实验所得出的实验结果是通 过多维空间的概率分布，来估算出指纹的匹配度的。所以具实验结 果具有不稳定性。
指纹特征点匹配算法主要是细节特征的匹配。依靠指纹本身决定的可靠参考坐标 系,可以提高指纹匹配的效率。指纹中心处具有很高的不可定向性程度,其附近的纹线方 向多变。据此,我们利用方向图和不可定向性图设计和实现了指纹自动定位的快速算法 。该算法能够确定指纹中心点的位置和方向,自动定位率在98%以上。对于用活体指纹 采集仪输入的指纹,自动定位率更高。用同样的方法,我们还可以准确提取指纹的下中心 及左、右三角点等形态特征与辅助定位信息。它要匹配的是指纹图像和预先存储图像 特征值。英国的专家亨利认为，只要13共同特征点存在的两个指纹图像的比例，就可 以认为这两个要比较指纹图像是相同的指纹。
Lecture 6 - Fingerprint Recognition
Hasan Fleyeh hfl@du.se hfl@du se Dalarna University
23/11/2010
Hasan Fleyeh
2
Introduction
A fingerprint is the representation of the epidermis of a finger. g It consists of a pattern of interleaved ridges and valleys. y The DNA gives the general instructions on the way skin should form in a development fetus, but the p , specific way it forms is a result of random events. This is the reason when even the fingerprints of g p identical twins are different.
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Formation of Fingerprints
The differentiation process is triggered by the growth in size of the volar pads on the palms, fingers, soles, and toes. The flow of amniotic fluids around the fetus and its position in the uterus change during the differentiation process. Thus the cells on the fingertip grow in a microenvironment that is slightly diff li h l different f from h d to h d and fi hand hand d finger to fi finger. The finer details of the fingerprints are determined by this changing microenvironment. A small difference in microenvironment is amplified by the differentiation process of the cells. There are so many variations during the formation of fingerprints that it would be virtually impossible for two fingerprints to be exactly alike. But, because the fingerprints are differentiated from the same genes, they are not totally random patterns either. h ll d ih
Lecture 8翻译技巧(词义的延伸)
英语中，特别在现代英语中，常常用一个表示具体形象 的词来表示一种属性、一个事物或一种概念。翻译这类 词时，一般可将其词义作抽象化的引伸，译文才能流畅、 自然。 将表示具体形象的词译成该形象所代表的属性的词 There is a mixture of the tiger and the ape in the character of the imperialists. 帝国主义者的性格既残暴，又狡猾。 这里把tiger（老虎）和ape（猿）这两个具体形象引伸 为这两个形象所代表的属性：“残暴”和“狡猾”。 Every life has its roses and thorns. 每个人的生活都有甜和苦。 这里把roses（玫瑰）和thorns（刺）这两个具体形象 引伸为这两个形象所代表的属性：“甜”和“苦”。
I have butterflies in my stomach. 我很紧张。 (8)In the modern world salt has many uses beyond the dining table. 在现代世界上，盐除了供食用外，还有许多其他 用途。（dining table原文为"饭桌"）
水译：有些书可供一尝，有些书可以吞下，有不多的几 部书则应当咀嚼消化；这就是说，有些书只要读读他们 的一部分就够了，有些书可以全读，但是不必过于细心 地读；还有不多的几部书则应当全读，勤读，而且用心 地读。 王译：书有可浅尝者，有可吞食者，少数则须咀嚼消化。 换言之，有只须读其部分者，有只须大体涉猎者，少数 则须全读，读时须全神贯注，孜孜不倦。
词义的具体化引伸 将词义作具体化的引申，就是把原文中的某些 比较抽象和笼统的词在译文中引申为意义比较 具体和明确的词。 英语中也有用代表抽象概念或属性的词来表示 一种具体事物，译成汉语时一般可作具体化引 伸。
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Hasan Fleyeh
4
Level 1 (The Global Level)
Ridges often run smoothly in parallel but exhibit one or more regions where they assume distinctive shapes characterized by
θ yo xo
yo
xo
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Ambiguity with Minutiae
In practice, an ambiguity exists between termination and bifurcation minutiae. Depending D di on the th finger fi pressure against the surface where h the h fingerprint fi i is i left, l f terminations may appear as bifurcation and vice versa.
Loop (shape like ∩ ) Delta (shape like Δ) Whorl (shape like O)
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Hasan Fleyeh
5
Level 1
Singular regions (white boxes) and core points (small circles) in fingerprint images
High curvature, Frequent ridge Terminations T i ti
These shapes are called as singularities or singular regions. They Th are classified l ifi d into i t three th types t
Level 1 (the overall global ridge flow pattern), pattern) Level 2 (minutiae points), Level 3 (pores, local shape of ridge edges, etc.)
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Fingerprint Analysis
Ridges g ( (Black Lines) )
Valleys (White Lines)
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Hasan Fleyeh
3
Ridge Details
Ridge details are generally described in a hierarchical order at three different levels, levels namely,
Fingerprint Analysis and Representation
Hasan Fleyeh hfl@du se hfl@du.se Dalarna University
Fingerprint Analysis
The most evident structural of a fingerprint is a pattern of interleaved ridges g and valleys y. In a fingerprint image, a ridge is the dark parts whereas valleys y are the bright g . Ridges vary in width from 100 µm for very thin to 300 µm for very µ y thick ridges. g Injuries, superficial burn, or cuts do not affect the underlying y g ridge g structure, , and the original g p pattern is duplicated in any new skin that grows.
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The Major Fingerprint Classes
Arch (A)
Tented Arch (T)
Right Loop (R)
Left Loop (L)
30/11/2010
Whorl (W)
Hasan Fleyeh
Double Loop (W)
9
Level 2 (The Minutiae)
Minutia means small detail and it refers to various ways the ridges can be discontinued. Galton (1822-1911) was the first person to categorized minutiae and to observe that they remain unchanged over an individual’s lifetime. Minutiae are the most commonly used features in automatic fingerprint matching. They are sometimes called “Galton details” in his honor. In fingerprint the number of minutiae can be higher than 100 However, a small number of minutiae (12–15) is sufficient to claim with high confidence that two fingerprint originate from the same finger. finger
pores
30/11/2010
Partially developed g ridges
Hasan Fleyeh
Creases
14
Level 3 (Sweat Pores)
If the fingerprint is acquired at a high resolution (1000dpi), it is possible to identify the sweat pores. Sweat S pores are 60-250 µm.
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Level 3
Further details can be extracted in the fingerprint pattern. They y include all dimensional attributes of the ridges g such as width, shape, edge contours, pores and scars
30/11/2010 Hasan Fleyeh 16
Fingerprint Image Processing
Sometimes features are not directly related to any physical p y trait ( (local orientation image g or filter responses). Features may be used either for matching or their computation may serve as an intermediate step for the derivation of other features. For example, some pre-processing and enhancement steps are often performed to simplify the task of minutia extraction.
30/11/2010
Hasan Fleyeh
15
Fingerprint Image Processing
Although some fingerprint techniques directly compare images g through g correlation based methods, , the gray g y scale image intensities are known to be unstable representation. Most of the fingerprint recognition and classification algorithms require a feature extraction stage for indentifying salient features. The features extracted from fingerprint images often have a direct physical counterpart (singularities or minutiae)
30/11/2010 Hasof Minutiae
30/11/2010
Hasan Fleyeh
11
The Minutiae
Each minutia is denoted by
its class, its it x- and d y-coordinates di t the angle between the t tangent t to t the th ridge id line li at the minutia position and the horizontal axis axis.