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The document discusses edge detection in image processing, focusing on three key aspects: edge direction, position, and strength. Edge direction refers to the angle of the edge relative to a reference axis, edge position indicates the coordinates of edge pixels, and edge strength quantifies the intensity change at the edge. These concepts are essential for identifying and analyzing features within images, particularly in tasks involving image processing algorithms.

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12 Edge Detection lecture 02 BY AHMED R. A. SHAMSAN MOHAMMED ALMOHAMADI AHMED R. A. SHAMSAN & M. MOHAMADI EDGE DETECTION | LUC01
13 Edge Descriptors  Edge Direction:  Specifies the angle or orientation of the edge relative to a reference axis (e.g., horizontal or vertical).  Edge Position:  Indicates the location of the edge within the image (coordinates of the edge pixel).  Edge Strength:  Quantifies the magnitude of the intensity change at the edge. 13 ‫الحافة‬ ‫واصفات‬ ‫اتجاه‬ ‫الحافة‬ : ‫يحدد‬ ‫زاوية‬ ‫أو‬ ‫اتجاه‬ ‫الحافة‬ ‫ﺑالﻨﺴﺒة‬ ‫إلى‬ ‫محور‬ ‫مﺮﺟﻌﻲ‬ ) ‫ﻋﻠى‬ ‫سﺒيل‬ ،‫المثال‬ ‫أف‬ ‫ﻘﻲ‬ ‫أو‬ ‫رأسﻲ‬ ( . ‫ﻣﻮﻗﻊ‬ ‫الحافة‬ : ‫يشيﺮ‬ ‫إلى‬ ‫موﻗﻊ‬ ‫الحافة‬ ‫داخل‬ ‫الصورة‬ ) ‫إحداثيات‬ ‫ﺑﻜﺴل‬ ‫الحافة‬ ( . ‫ﻗﻮة‬ ‫الحافة‬ : ‫يحدد‬ ‫حجﻢ‬ ‫تغيﺮ‬ ‫الشدة‬ ‫ﻋﻨد‬ ‫الحافة‬ . AHMED R. A. SHAMSAN & M. MOHAMADI EDGE DETECTION | LUC01
Edge Direction the concept of Edge Direction in the context of image processing. • Edge Direction is a fundamental concept in edge detection algorithms. It refers to the orientation or angle of an edge in an image relative to a reference axis, typically the horizontal or vertical axis. • For instance, consider an image with various shapes like squares, rectangles, and circles. Each shape has edges, and these edges have a specific direction or orientation. This direction is measured as an angle relative to a reference axis. • Here are some examples: • A horizontal edge has a direction of 0 degrees or 180 degrees relative to the vertical axis. • A vertical edge has a direction of 90 degrees or 270 degrees relative to the horizontal axis. • An edge that is diagonal from bottom-left to top-right has a direction of 45 degrees or 225 degrees. • An edge that is diagonal from top-left to bottom-right has a direction of 135 degrees or 315 degrees. • These angles can vary depending on the orientation of the edge. The edge direction is a crucial factor in many image processing tasks, as it helps in identifying and classifying different features in the image. ‫ﻣفهﻮم‬ Edge Direction ‫فﻲ‬ ‫سياق‬ ‫ﻣﻌالجة‬ ‫الصﻮر‬ . ‫هو‬ ‫مفهوم‬ ‫أساسﻲ‬ ‫فﻲ‬ ‫خوارزميات‬ ‫اكتشاف‬ ‫الحافة‬ . ‫يشيﺮ‬ ‫إلى‬ ‫اتجاه‬ ‫أو‬ ‫زاوية‬ ‫الحافة‬ ‫ف‬ ‫ﻲ‬ ‫الصورة‬ ‫ﺑالﻨﺴﺒة‬ ‫إلى‬ ‫المحور‬ ،‫المﺮﺟﻌﻲ‬ ‫وﻋادة‬ ‫ما‬ ‫يﻜون‬ ‫المحور‬ ‫اﻷفﻘﻲ‬ ‫أو‬ ‫الﺮأسﻲ‬ . ‫ﻋﻠى‬ ‫سﺒيل‬ ،‫المثال‬ ‫ﺿﻊ‬ ‫فﻲ‬ ‫اﻋتﺒارك‬ ‫صورة‬ ‫ذات‬ ‫أشﻜال‬ ‫مﺨتﻠفة‬ ‫مثل‬ ‫المﺮﺑﻌات‬ ‫والمﺴتطي‬ ‫ﻼت‬ ‫والدوائﺮ‬ . ‫كل‬ ‫شﻜل‬ ‫له‬ ،‫حواف‬ ‫وهذه‬ ‫الحواف‬ ‫لها‬ ‫اتجاه‬ ‫أو‬ ‫اتجاه‬ ‫محدد‬ . ‫يﻘاس‬ ‫هذا‬ ‫اﻻتجاه‬ ‫كزاوية‬ ‫ﻧﺴﺒ‬ ‫ة‬ ‫إلى‬ ‫المحور‬ ‫المﺮﺟﻌﻲ‬ . ‫فيما‬ ‫يﻠﻲ‬ ‫ﺑﻌﺾ‬ ‫اﻷمثﻠة‬ : • ‫الحافة‬ ‫اﻷفﻘية‬ ‫لها‬ ‫اتجاه‬ 0 ‫درﺟة‬ ‫أو‬ 180 ‫درﺟة‬ ‫ﺑالﻨﺴﺒة‬ ‫لﻠمحور‬ ‫الﺮأسﻲ‬ . • ‫الحافة‬ ‫الﺮأسية‬ ‫لها‬ ‫اتجاه‬ 90 ‫درﺟة‬ ‫أو‬ 270 ‫درﺟة‬ ‫ﺑالﻨﺴﺒة‬ ‫لﻠمحور‬ ‫اﻷفﻘﻲ‬ . • ‫الحافة‬ ‫التﻲ‬ ‫تﻜون‬ ‫ﻗطﺮية‬ ‫مﻦ‬ ‫أسفل‬ ‫اليﺴار‬ ‫إلى‬ ‫أﻋﻠى‬ ‫اليميﻦ‬ ‫لها‬ ‫اتجاه‬ 45 ‫درﺟة‬ ‫أو‬ 225 ‫درﺟة‬ . • ‫الحافة‬ ‫التﻲ‬ ‫تﻜون‬ ‫ﻗطﺮية‬ ‫مﻦ‬ ‫أﻋﻠى‬ ‫اليﺴار‬ ‫إلى‬ ‫أسفل‬ ‫اليميﻦ‬ ‫لها‬ ‫اتجاه‬ 135 ‫درﺟة‬ ‫أو‬ 315 ‫درﺟة‬ . • ‫يمﻜﻦ‬ ‫أن‬ ‫تﺨتﻠﻒ‬ ‫هذه‬ ‫الزوايا‬ ‫ًا‬‫د‬‫اﻋتما‬ ‫ﻋﻠى‬ ‫اتجاه‬ ‫الحافة‬ . ‫يﻌد‬ ‫اتجاه‬ ‫الحافة‬ ً‫ﻼ‬‫ﻋام‬ ‫ا‬ً‫م‬‫حاس‬ ‫ف‬ ‫ﻲ‬ ‫الﻌديد‬ ‫مﻦ‬ ‫مهام‬ ‫مﻌالجة‬ ،‫الصور‬ ‫ﻷﻧه‬ ‫يﺴاﻋد‬ ‫فﻲ‬ ‫تحديد‬ ‫وتصﻨيﻒ‬ ‫الميزات‬ ‫المﺨتﻠفة‬ ‫فﻲ‬ ‫الصورة‬ . EDGE DETECTION | LUC01 AHMED R. A. SHAMSAN & M. MOHAMADI 14
Edge Position  In simple terms, Edge Position refers to the specific location of an edge within an image. This location is typically identified by the coordinates of the pixels that make up that edge.  For example, consider an image as a grid of pixels. Each pixel has a unique position, defined by its coordinates (x, y), where x is the horizontal position and y is the vertical position.  When we talk about the “Edge Position”, we are referring to the coordinates of the pixels that form the edge in this grid. These edge pixels are usually where there is a significant change in color or intensity in the image, indicating a boundary or a change in the object within the image.  So, if you have an edge in an image, the “Edge Position” would tell you exactly where that edge is located within the image grid. This is crucial in many image processing tasks, as it helps in identifying and analyzing different objects and features in the image. ‫ﺑﻌﺒارات‬ ،‫ﺑﺴيطة‬ ‫يشيﺮ‬ Edge Position ‫إلى‬ ‫الموﻗﻊ‬ ‫المحدد‬ ‫لﻠحافة‬ ‫داخل‬ ‫الصورة‬ . ‫يتﻢ‬ ‫تحديد‬ ‫هذا‬ ‫الموﻗﻊ‬ ً‫ة‬‫ﻋاد‬ ‫مﻦ‬ ‫خﻼل‬ ‫إحداثيات‬ ‫الﺒﻜﺴﻼت‬ ‫التﻲ‬ ‫تشﻜل‬ ‫تﻠﻚ‬ ‫الحافة‬ . ‫ﻋﻠى‬ ‫سﺒيل‬ ،‫المثال‬ ‫ﺿﻊ‬ ‫فﻲ‬ ‫اﻋتﺒارك‬ ‫الصورة‬ ‫كشﺒﻜة‬ ‫مﻦ‬ ‫الﺒﻜﺴﻼت‬ . ‫كل‬ ‫ﺑﻜﺴل‬ ‫له‬ ‫موﻗﻊ‬ ‫ف‬ ،‫ﺮيد‬ ‫محدد‬ ‫ﺑإحداثياته‬ ) x, y) ، ‫حيث‬ x ‫هو‬ ‫الموﺿﻊ‬ ‫اﻷفﻘﻲ‬ ‫و‬ y ‫هو‬ ‫الموﺿﻊ‬ ‫الﺮأسﻲ‬ . ‫ﻋﻨدما‬ ‫ﻧتحدث‬ ‫ﻋﻦ‬ » ‫موﻗﻊ‬ ‫الحافة‬ « ، ‫فإﻧﻨا‬ ‫ﻧشيﺮ‬ ‫إلى‬ ‫إحداثيات‬ ‫الﺒﻜﺴﻼت‬ ‫التﻲ‬ ‫تشﻜل‬ ‫الحاف‬ ‫ة‬ ‫فﻲ‬ ‫هذه‬ ‫الشﺒﻜة‬ . ‫ﻋادة‬ ‫ما‬ ‫تﻜون‬ ‫هذه‬ ‫الﺒﻜﺴﻼت‬ ‫الحافة‬ ‫حيث‬ ‫يﻜون‬ ‫هﻨاك‬ ‫تغييﺮ‬ ‫كﺒيﺮ‬ ‫فﻲ‬ ‫الﻠون‬ ‫أو‬ ‫الش‬ ‫دة‬ ‫فﻲ‬ ،‫الصورة‬ ‫مما‬ ‫يشيﺮ‬ ‫إلى‬ ‫حد‬ ‫أو‬ ‫تغييﺮ‬ ‫فﻲ‬ ‫الﻜائﻦ‬ ‫داخل‬ ‫الصورة‬ . ،‫لذا‬ ‫إذا‬ ‫كان‬ ‫لديﻚ‬ ‫ميزة‬ ‫فﻲ‬ ،‫الصورة‬ ‫فإن‬ » ‫موﻗﻊ‬ ‫الحافة‬ « ‫سيﺨﺒﺮك‬ ‫ﺑالﻀﺒﻂ‬ ‫ﺑمﻜان‬ ‫وﺟود‬ ‫هذه‬ ‫ا‬ ‫لحافة‬ ‫داخل‬ ‫شﺒﻜة‬ ‫الصور‬ . ‫هذا‬ ‫أمﺮ‬ ‫ﺑالﻎ‬ ‫اﻷهمية‬ ‫فﻲ‬ ‫الﻌديد‬ ‫مﻦ‬ ‫مهام‬ ‫مﻌالجة‬ ،‫الصور‬ ‫ﻷﻧه‬ ‫يﺴاﻋد‬ ‫فﻲ‬ ‫تح‬ ‫ديد‬ ‫وتحﻠيل‬ ‫اﻷشياء‬ ‫والميزات‬ ‫المﺨتﻠفة‬ ‫فﻲ‬ ‫الصورة‬ . EDGE DETECTION | LUC01 AHMED R. A. SHAMSAN & M. MOHAMADI 15
Edge Strength  the concept of Edge Strength in image processing.  In simple terms, Edge Strength is a measure of how “sharp” or “strong” an edge is in an image. It quantifies the magnitude of the change in intensity at the edge.  Imagine you’re looking at a black-and-white image. The intensity of each pixel in the image is represented by a grayscale value, with black being the lowest intensity and white being the highest. Now, if you have an edge in the image, this edge is usually where there is a significant change in these grayscale values - that is, a change from a darker area (lower intensity) to a lighter area (higher intensity), or vice versa.  The Edge Strength is a measure of how big this change in intensity is. If the change is very sudden and large (for example, a transition from black to white), the edge is considered “strong” and will have a high Edge Strength value. On the other hand, if the change is gradual or small (for example, a transition from dark gray to light gray), the edge is considered “weak” and will have a low Edge Strength value.  This concept is crucial in many image processing tasks, as it helps in identifying and distinguishing different features in the image based on the sharpness or strength of their edges. ‫الصور‬ ‫معالجة‬ ‫في‬ ‫الحافة‬ ‫قوة‬ ‫مفهوم‬ . ‫ﺑﻌﺒارات‬ ،‫ﺑﺴيطة‬ Edge Strength ‫هو‬ ‫مﻘياس‬ ‫لمدى‬ ‫وﺟود‬ ‫حافة‬ » ‫حادة‬ « ‫أو‬ » ‫ﻗوية‬ « ‫فﻲ‬ ‫الصورة‬ . ‫إﻧه‬ ‫يحدد‬ ‫حجﻢ‬ ‫التغيﺮ‬ ‫فﻲ‬ ‫الشدة‬ ‫ﻋﻨد‬ ‫الحافة‬ . ‫تﺨيل‬ ‫أﻧﻚ‬ ‫تﻨﻈﺮ‬ ‫إلى‬ ‫صورة‬ ‫ﺑاﻷﺑيﺾ‬ ‫واﻷسود‬ . ‫يتﻢ‬ ‫تمثيل‬ ‫شدة‬ ‫كل‬ ‫ﺑﻜﺴل‬ ‫فﻲ‬ ‫الص‬ ‫ورة‬ ‫ﺑﻘيمة‬ ،‫رمادية‬ ‫حيث‬ ‫يﻜون‬ ‫الﻠون‬ ‫اﻷسود‬ ‫هو‬ ‫اﻷﻗل‬ ‫شدة‬ ‫واﻷﺑيﺾ‬ ‫هو‬ ‫اﻷﻋﻠى‬ . ،‫اﻵن‬ ‫إذا‬ ‫كان‬ ‫لديﻚ‬ ‫ميزة‬ ‫فﻲ‬ ،‫الصورة‬ ‫فهذه‬ ‫الحافة‬ ‫ﻋادة‬ ‫ما‬ ‫تﻜون‬ ‫حيث‬ ‫يوﺟد‬ ‫تغييﺮ‬ ‫كﺒيﺮ‬ ‫فﻲ‬ ‫هذه‬ ‫الﻘيﻢ‬ ‫الﺮمادية‬ - ‫أي‬ ‫تغييﺮ‬ ‫مﻦ‬ ‫مﻨطﻘة‬ ‫أكثﺮ‬ ‫ﻗتامة‬ ) ‫شدة‬ ‫أﻗل‬ ( ‫إلى‬ ‫مﻨطﻘة‬ ‫أخﻒ‬ ) ‫كثافة‬ ‫أﻋﻠى‬ ( ، ‫أو‬ ‫الﻌﻜس‬ . ‫ﻗوة‬ ‫الحافة‬ ‫هﻲ‬ ‫مﻘياس‬ ‫لحجﻢ‬ ‫هذا‬ ‫التغييﺮ‬ ‫فﻲ‬ ‫الشدة‬ . ‫إذا‬ ‫كان‬ ‫التغييﺮ‬ ‫ا‬ً‫ﺌ‬‫مفاﺟ‬ ‫وكﺒي‬ ‫ا‬ً‫ﺮ‬ ‫ًا‬‫د‬‫ﺟ‬ ) ‫ﻋﻠى‬ ‫سﺒيل‬ ،‫المثال‬ ‫اﻻﻧتﻘال‬ ‫مﻦ‬ ‫اﻷسود‬ ‫إلى‬ ‫اﻷﺑيﺾ‬ ( ، ‫فإن‬ ‫الحافة‬ ‫تﻌتﺒﺮ‬ » ‫ﻗوية‬ « ‫وست‬ ‫ﻜون‬ ‫لها‬ ‫ﻗيمة‬ ‫ﻋالية‬ ‫لﻘوة‬ ‫الحافة‬ . ‫مﻦ‬ ‫ﻧاحية‬ ،‫أخﺮى‬ ‫إذا‬ ‫كان‬ ‫التغييﺮ‬ ‫ا‬ً‫ي‬‫تدريج‬ ‫أو‬ ‫ا‬ً‫صغيﺮ‬ ) ‫ﻋﻠى‬ ‫س‬ ‫ﺒيل‬ ،‫المثال‬ ‫اﻻﻧتﻘال‬ ‫مﻦ‬ ‫الﺮمادي‬ ‫الداكﻦ‬ ‫إلى‬ ‫الﺮمادي‬ ‫الفاتح‬ ( ، ‫فإن‬ ‫الحافة‬ ‫تﻌتﺒﺮ‬ » ‫ﺿﻌيفة‬ « ‫وس‬ ‫تﻜون‬ ‫لها‬ ‫ﻗيمة‬ ‫مﻨﺨفﻀة‬ ‫لﻘوة‬ ‫الحافة‬ . ‫هذا‬ ‫المفهوم‬ ‫حاسﻢ‬ ‫فﻲ‬ ‫الﻌديد‬ ‫مﻦ‬ ‫مهام‬ ‫مﻌالجة‬ ،‫الصور‬ ‫ﻷﻧه‬ ‫يﺴاﻋد‬ ‫فﻲ‬ ‫تحديد‬ ‫وتمييز‬ ‫ال‬ ‫ميزات‬ ‫المﺨتﻠفة‬ ‫فﻲ‬ ‫الصورة‬ ً‫ء‬‫ﺑﻨا‬ ‫ﻋﻠى‬ ‫حدة‬ ‫أو‬ ‫ﻗوة‬ ‫حوافها‬ . EDGE DETECTION | LUC01 AHMED R. A. SHAMSAN & M. MOHAMADI 16
17 Modeling Intensity Changes  Step edge: the image intensity abruptly changes from one value on one side of the discontinuity to a different value on the opposite side. ‫النمذجة‬ ‫شدة‬ ‫تغييرات‬ ‫ﺣافة‬ ‫الخطﻮة‬ : ‫تتغيﺮ‬ ‫شدة‬ ‫الصورة‬ ‫فجأة‬ ‫مﻦ‬ ‫ﻗيمة‬ ‫واحدة‬ ‫ﻋﻠى‬ ‫ﺟاﻧﺐ‬ ‫واحد‬ ‫مﻦ‬ ‫اﻻﻧﻘطاع‬ ‫إل‬ ‫ى‬ ‫ﻗيمة‬ ‫مﺨتﻠفة‬ ‫ﻋﻠى‬ ‫الجاﻧﺐ‬ ‫اﻵخﺮ‬ . AHMED R. A. SHAMSAN & M. MOHAMADI EDGE DETECTION | LUC01
18 Step edge  the concept of a “Step Edge” in image processing into simple points:  Image Intensity: This refers to the brightness or darkness of a pixel in an image. It can vary from low (dark) to high (bright).  Edge: In an image, an edge is a boundary between two regions with different intensities. For example, the boundary between a black square and a white background forms an edge.  Step Edge: This is a type of edge where the intensity changes abruptly from one side to the other.  Let’s illustrate this with an example:  Imagine a black-and-white image of a square. The square is black, and the background is white.  The edge of the square is a boundary where the intensity changes from black (low intensity) to white (high intensity).  This change in intensity is abrupt, meaning it happens suddenly. On one side of the edge, you have the black square (low intensity), and on the other side, you have the white background (high intensity).  This sudden change in intensity is what we call a “Step Edge”.  In summary, a “Step Edge” in an image is a boundary where the intensity changes suddenly from one value to another. ‫مفهوم‬ » ‫حافة‬ ‫الﺨطوة‬ « ‫فﻲ‬ ‫مﻌالجة‬ ‫الصور‬ ‫إلى‬ ‫ﻧﻘاط‬ ‫ﺑﺴيطة‬ : • ‫شدة‬ ‫الصﻮرة‬ : ‫يشيﺮ‬ ‫هذا‬ ‫إلى‬ ‫سطوع‬ ‫أو‬ ‫ظﻼم‬ ‫الﺒﻜﺴل‬ ‫فﻲ‬ ‫الصورة‬ . ‫يمﻜﻦ‬ ‫أن‬ ‫يﺨتﻠﻒ‬ ‫مﻦ‬ ‫مﻨﺨ‬ ‫فﺾ‬ ) ‫مﻈﻠﻢ‬ ( ‫إلى‬ ‫مﺮتفﻊ‬ ) ‫مشﺮق‬ ( . • ‫الحافة‬ : ‫فﻲ‬ ،‫الصورة‬ ‫الحافة‬ ‫هﻲ‬ ‫حدود‬ ‫ﺑيﻦ‬ ‫مﻨطﻘتيﻦ‬ ‫ﺑﻜثافة‬ ‫مﺨتﻠفة‬ . ‫ﻋﻠى‬ ‫سﺒيل‬ ‫المث‬ ،‫ال‬ ‫تشﻜل‬ ‫الحدود‬ ‫ﺑيﻦ‬ ‫المﺮﺑﻊ‬ ‫اﻷسود‬ ‫والﺨﻠفية‬ ‫الﺒيﻀاء‬ ‫حافة‬ . • Step Edge: ‫هذا‬ ‫ﻧوع‬ ‫مﻦ‬ ‫الحافة‬ ‫حيث‬ ‫تتغيﺮ‬ ‫الشدة‬ ‫فجأة‬ ‫مﻦ‬ ‫ﺟاﻧﺐ‬ ‫إلى‬ ‫آخﺮ‬ . ‫دﻋوﻧا‬ ‫ﻧوﺿح‬ ‫هذا‬ ‫ﺑمثال‬ : • ‫تﺨيل‬ ‫صورة‬ ‫ﺑاﻷﺑيﺾ‬ ‫واﻷسود‬ ‫لمﺮﺑﻊ‬ . ‫المﺮﺑﻊ‬ ،‫أسود‬ ‫والﺨﻠفية‬ ‫ﺑيﻀاء‬ . • ‫حافة‬ ‫المﺮﺑﻊ‬ ‫هﻲ‬ ‫حدود‬ ‫حيث‬ ‫تتغيﺮ‬ ‫الشدة‬ ‫مﻦ‬ ‫اﻷسود‬ ) ‫مﻨﺨفﺾ‬ ‫الﻜثافة‬ ( ‫إلى‬ ‫اﻷﺑيﺾ‬ ) ‫ﻋا‬ ‫لﻲ‬ ‫الﻜثافة‬ ( . • ‫هذا‬ ‫التغييﺮ‬ ‫فﻲ‬ ‫الشدة‬ ،‫مفاﺟﺊ‬ ‫مما‬ ‫يﻌﻨﻲ‬ ‫أﻧه‬ ‫يحدث‬ ‫فجأة‬ . ‫ﻋﻠى‬ ‫ﺟاﻧﺐ‬ ‫واحد‬ ‫مﻦ‬ ،‫الحافة‬ ‫لديﻚ‬ ‫المﺮﺑﻊ‬ ‫اﻷسود‬ ) ‫كثافة‬ ‫مﻨﺨفﻀة‬ ( ، ‫وﻋﻠى‬ ‫الجاﻧﺐ‬ ،‫اﻵخﺮ‬ ‫لديﻚ‬ ‫الﺨﻠفية‬ ‫الﺒيﻀاء‬ ) ‫كثافة‬ ‫ﻋالية‬ ( . • ‫هذا‬ ‫التغييﺮ‬ ‫المفاﺟﺊ‬ ‫فﻲ‬ ‫الشدة‬ ‫هو‬ ‫ما‬ ‫ﻧﺴميه‬ » Step Edge». • ،‫ﺑاختصار‬ ‫فإن‬ » Step Edge» ‫فﻲ‬ ‫الصورة‬ ‫هﻲ‬ ‫حدود‬ ‫تتغيﺮ‬ ‫فيها‬ ‫الشدة‬ ‫فجأة‬ ‫مﻦ‬ ‫ﻗيمة‬ ‫إلى‬ ‫أخﺮ‬ ‫ى‬ . AHMED R. A. SHAMSAN & M. MOHAMADI EDGE DETECTION | LUC01
19 Modeling Intensity Changes (contd)  Ramp edge:  a step edge where the intensity change is not instantaneous but occurs over a finite distance. ‫النمذجة‬ ‫شدة‬ ‫تغييرات‬ ‫المنحدر‬ ‫ﺣافة‬ : ‫مح‬ ‫مﺴافة‬ ‫ﻋﻠى‬ ‫يحدث‬ ‫ولﻜﻨه‬ ‫ا‬ً‫ي‬‫فور‬ ‫ليس‬ ‫الشدة‬ ‫تغيﺮ‬ ‫حيث‬ ‫خطوة‬ ‫حافة‬ ‫دودة‬ AHMED R. A. SHAMSAN & M. MOHAMADI EDGE DETECTION | LUC01
Ramp edge  the concept of a “Ramp Edge” in image processing into simple points: 1. Image Intensity: This refers to the brightness or darkness of a pixel in an image. It can vary from low (dark) to high (bright). 2. Edge: In an image, an edge is a boundary between two regions with different intensities. For example, the boundary between a black square and a white background forms an edge. 3. Step Edge: This is a type of edge where the intensity changes abruptly from one side to the other. 4. Ramp Edge: Unlike a step edge, a ramp edge is where the intensity change is not instantaneous but occurs over a finite distance.  Let’s illustrate this with an example: • Imagine a black-and-white image of a gradient. The gradient transitions from black to white. • The edge of this gradient is a boundary where the intensity changes from black (low intensity) to white (high intensity). • However, this change in intensity is not abrupt, but gradual. It happens over a distance, not at a single point. This is what we call a “Ramp Edge”.  In summary, a “Ramp Edge” in an image is a boundary where the intensity changes gradually from one value to another over a certain distance. This concept is crucial in image processing tasks such as edge detection and image segmentation, especially when dealing with images that have gradual transitions in intensity. ‫ﻣفهﻮم‬ » ‫ﺣافة‬ ‫المنحدر‬ « ‫فﻲ‬ ‫ﻣﻌالجة‬ ‫الصﻮر‬ ‫إلى‬ ‫نقاط‬ ‫بسيطة‬ : • ‫شدة‬ ‫الصﻮرة‬ : ‫يشيﺮ‬ ‫هذا‬ ‫إلى‬ ‫سطوع‬ ‫أو‬ ‫ظﻼم‬ ‫الﺒﻜﺴل‬ ‫فﻲ‬ ‫الصورة‬ . ‫يمﻜﻦ‬ ‫أن‬ ‫يﺨتﻠﻒ‬ ‫مﻦ‬ ‫مﻨﺨ‬ ‫فﺾ‬ ) ‫مﻈﻠﻢ‬ ( ‫إلى‬ ‫مﺮتفﻊ‬ ) ‫مشﺮق‬ ( . • ‫الحافة‬ : ‫فﻲ‬ ،‫الصورة‬ ‫الحافة‬ ‫هﻲ‬ ‫حدود‬ ‫ﺑيﻦ‬ ‫مﻨطﻘتيﻦ‬ ‫ﺑﻜثافة‬ ‫مﺨتﻠفة‬ . ‫ﻋﻠى‬ ‫سﺒيل‬ ‫المث‬ ،‫ال‬ ‫تشﻜل‬ ‫الحدود‬ ‫ﺑيﻦ‬ ‫المﺮﺑﻊ‬ ‫اﻷسود‬ ‫والﺨﻠفية‬ ‫الﺒيﻀاء‬ ‫حافة‬ . • Step Edge: ‫هذا‬ ‫ﻧوع‬ ‫مﻦ‬ ‫الحافة‬ ‫حيث‬ ‫تتغيﺮ‬ ‫الشدة‬ ‫فجأة‬ ‫مﻦ‬ ‫ﺟاﻧﺐ‬ ‫إلى‬ ‫آخﺮ‬ . • ‫ﺣافة‬ ‫المنحدر‬ : ‫ﻋﻠى‬ ‫ﻋﻜس‬ ‫حافة‬ ،‫الﺨطوة‬ ‫فإن‬ ‫حافة‬ ‫المﻨحدر‬ ‫هﻲ‬ ‫المﻜان‬ ‫الذي‬ ‫ﻻ‬ ‫يﻜون‬ ‫فيه‬ ‫تغ‬ ‫ييﺮ‬ ‫الشدة‬ ‫ا‬ً‫ي‬‫فور‬ ‫ولﻜﻨه‬ ‫يحدث‬ ‫ﻋﻠى‬ ‫مﺴافة‬ ‫محدودة‬ . ‫دﻋوﻧا‬ ‫ﻧوﺿح‬ ‫هذا‬ ‫ﺑمثال‬ : • ‫تﺨيل‬ ‫صورة‬ ‫ﺑاﻷﺑيﺾ‬ ‫واﻷسود‬ ‫لﻠتدرج‬ . ‫يﻨتﻘل‬ ‫التدرج‬ ‫مﻦ‬ ‫اﻷسود‬ ‫إلى‬ ‫اﻷﺑيﺾ‬ . • ‫حافة‬ ‫هذا‬ ‫التدرج‬ ‫هﻲ‬ ‫حدود‬ ‫حيث‬ ‫تتغيﺮ‬ ‫الشدة‬ ‫مﻦ‬ ‫اﻷسود‬ ) ‫مﻨﺨفﺾ‬ ‫الﻜثافة‬ ( ‫إلى‬ ‫اﻷ‬ ‫ﺑيﺾ‬ ) ‫ﻋالﻲ‬ ‫الﻜثافة‬ ( . ‫ومﻊ‬ ،‫ذلﻚ‬ ‫فإن‬ ‫هذا‬ ‫التغييﺮ‬ ‫فﻲ‬ ‫الشدة‬ ‫ليس‬ ،‫ا‬ً‫ﺌ‬‫مفاﺟ‬ ‫ولﻜﻨه‬ ‫تدريجﻲ‬ . ‫يحدث‬ ‫ذلﻚ‬ ‫ﻋ‬ ‫ﻠى‬ ،‫مﺴافة‬ ‫وليس‬ ‫فﻲ‬ ‫ﻧﻘطة‬ ‫واحدة‬ . ‫هذا‬ ‫ما‬ ‫ﻧﺴميه‬ » ‫حافة‬ ‫المﻨحدر‬ « . • ،‫ﺑاختصار‬ ‫فإن‬ » ‫حافة‬ ‫المﻨحدر‬ « ‫فﻲ‬ ‫الصورة‬ ‫هﻲ‬ ‫حدود‬ ‫تتغيﺮ‬ ‫فيها‬ ‫الشدة‬ ‫تدريج‬ ‫ا‬ً‫ي‬ ‫مﻦ‬ ‫ﻗيمة‬ ‫إلى‬ ‫أخﺮى‬ ‫ﻋﻠى‬ ‫مﺴافة‬ ‫مﻌيﻨة‬ . ‫هذا‬ ‫المفهوم‬ ‫حاسﻢ‬ ‫فﻲ‬ ‫مهام‬ ‫مﻌالجة‬ ‫الصور‬ ‫مثل‬ ‫اكتشاف‬ ‫الحافة‬ ‫وتجزئة‬ ،‫الصورة‬ ‫خاصة‬ ‫ﻋﻨد‬ ‫التﻌامل‬ ‫مﻊ‬ ‫الصور‬ ‫التﻲ‬ ‫لها‬ ‫اﻧتﻘاﻻ‬ ‫ت‬ ‫تدريجية‬ ‫فﻲ‬ ‫الشدة‬ . EDGE DETECTION | LUC01 AHMED R. A. SHAMSAN & M. MOHAMADI 20
21 Modeling Intensity Changes (contd)  Roof edge: a ridge edge where the intensity change is not instantaneous but occurs over a finite distance (i.e., usually generated by the intersection of two surfaces). ‫السقف‬ ‫ﺣافة‬ : ‫محدودة‬ ‫مﺴافة‬ ‫ﻋﻠى‬ ‫يحدث‬ ‫ولﻜﻨه‬ ‫ا‬ً‫ي‬‫فور‬ ‫الشدة‬ ‫تغييﺮ‬ ‫يﻜون‬ ‫ﻻ‬ ‫حيث‬ ‫التﻼل‬ ‫حافة‬ ) ‫إﻧ‬ ‫يتﻢ‬ ‫ما‬ ‫ﻋادة‬ ‫أي‬ ‫ﻋﻦ‬ ‫شاؤه‬ ‫سطحيﻦ‬ ‫تﻘاطﻊ‬ ‫طﺮيق‬ .( AHMED R. A. SHAMSAN & M. MOHAMADI EDGE DETECTION | LUC01
22 Roof edge  the concept of a “Roof Edge” in image processing into simple points: 1. Image Intensity: This refers to the brightness or darkness of a pixel in an image. It can vary from low (dark) to high (bright). 2. Edge: In an image, an edge is a boundary between two regions with different intensities. For example, the boundary between a black square and a white background forms an edge. 3. Ridge Edge: This is a type of edge where the intensity changes gradually from one side to the other, similar to a ramp edge. 4. Roof Edge: A roof edge is a special type of ridge edge. It is usually formed by the intersection of two surfaces. The intensity change is not instantaneous but occurs over a finite distance.  Let’s illustrate this with an example: • Imagine a black-and-white image of a pyramid. The edges of the pyramid are formed by the intersection of two surfaces. • The edge of this pyramid is a boundary where the intensity changes from black (low intensity) to white (high intensity). • However, this change in intensity is not abrupt, but gradual. It happens over a distance, not at a single point. This is what we call a “Roof Edge”.  In summary, a “Roof Edge” in an image is a boundary where the intensity changes gradually from one value to another over a certain distance, typically formed by the intersection of two surfaces. This concept is crucial in image processing tasks such as edge detection and image segmentation, especially when dealing with images that have complex structures and features. ‫ﻣفهﻮم‬ » ‫ﺣافة‬ ‫السقف‬ « ‫فﻲ‬ ‫ﻣﻌالجة‬ ‫الصﻮر‬ ‫إلى‬ ‫نقاط‬ ‫بسيطة‬ : • ‫شدة‬ ‫الصﻮرة‬ : ‫يشيﺮ‬ ‫هذا‬ ‫إلى‬ ‫سطوع‬ ‫أو‬ ‫ظﻼم‬ ‫الﺒﻜﺴل‬ ‫فﻲ‬ ‫الصورة‬ . ‫يمﻜﻦ‬ ‫أن‬ ‫يﺨتﻠﻒ‬ ‫مﻦ‬ ‫مﻨﺨ‬ ‫فﺾ‬ ) ‫مﻈﻠﻢ‬ ( ‫إلى‬ ‫مﺮتفﻊ‬ ) ‫مشﺮق‬ ( . • ‫الحافة‬ : ‫فﻲ‬ ،‫الصورة‬ ‫الحافة‬ ‫هﻲ‬ ‫حدود‬ ‫ﺑيﻦ‬ ‫مﻨطﻘتيﻦ‬ ‫ﺑﻜثافة‬ ‫مﺨتﻠفة‬ . ‫ﻋﻠى‬ ‫سﺒيل‬ ‫المث‬ ،‫ال‬ ‫تشﻜل‬ ‫الحدود‬ ‫ﺑيﻦ‬ ‫المﺮﺑﻊ‬ ‫اﻷسود‬ ‫والﺨﻠفية‬ ‫الﺒيﻀاء‬ ‫حافة‬ . • ‫ﺣافة‬ ‫التﻼل‬ : ‫هذا‬ ‫ﻧوع‬ ‫مﻦ‬ ‫الحافة‬ ‫حيث‬ ‫تتغيﺮ‬ ‫الشدة‬ ‫ا‬ً‫ي‬‫تدريج‬ ‫مﻦ‬ ‫ﺟاﻧﺐ‬ ‫إلى‬ ،‫آخﺮ‬ ‫ﻋﻠى‬ ‫غﺮا‬ ‫ر‬ ‫حافة‬ ‫المﻨحدر‬ . • ‫ﺣافة‬ ‫السقف‬ : ‫حافة‬ ‫الﺴﻘﻒ‬ ‫هﻲ‬ ‫ﻧوع‬ ‫خاص‬ ‫مﻦ‬ ‫حافة‬ ‫التﻼل‬ . ‫يتﻜون‬ ‫ﻋادة‬ ‫مﻦ‬ ‫تﻘاطﻊ‬ ‫سطحيﻦ‬ . ‫تغييﺮ‬ ‫الشدة‬ ‫ليس‬ ‫ا‬ً‫ي‬‫فور‬ ‫ولﻜﻨه‬ ‫يحدث‬ ‫ﻋﻠى‬ ‫مﺴافة‬ ‫محدودة‬ . ‫دﻋوﻧا‬ ‫ﻧوﺿح‬ ‫هذا‬ ‫ﺑمثال‬ : • ‫تﺨيل‬ ‫صورة‬ ‫ﺑاﻷﺑيﺾ‬ ‫واﻷسود‬ ‫لهﺮم‬ . ‫تتشﻜل‬ ‫حواف‬ ‫الهﺮم‬ ‫ﻋﻦ‬ ‫طﺮيق‬ ‫تﻘاطﻊ‬ ‫سطح‬ ‫يﻦ‬ . ‫حافة‬ ‫هذا‬ ‫الهﺮم‬ ‫هﻲ‬ ‫حدود‬ ‫حيث‬ ‫تتغيﺮ‬ ‫الشدة‬ ‫مﻦ‬ ‫اﻷسود‬ ) ‫مﻨﺨفﺾ‬ ‫الﻜثافة‬ ( ‫إلى‬ ‫اﻷﺑ‬ ‫يﺾ‬ ) ‫ﻋالﻲ‬ ‫الﻜثافة‬ ( . ‫ومﻊ‬ ،‫ذلﻚ‬ ‫فإن‬ ‫هذا‬ ‫التغييﺮ‬ ‫فﻲ‬ ‫الشدة‬ ‫ليس‬ ،‫ا‬ً‫ﺌ‬‫مفاﺟ‬ ‫ولﻜﻨه‬ ‫تدريجﻲ‬ . ‫يحدث‬ ‫ذلﻚ‬ ‫ﻋﻠى‬ ،‫مﺴافة‬ ‫وليس‬ ‫فﻲ‬ ‫ﻧﻘطة‬ ‫واحدة‬ . ‫هذا‬ ‫ما‬ ‫ﻧﺴميه‬ » ‫حافة‬ ‫الﺴﻘﻒ‬ « . • ،‫ﺑاختصار‬ ‫فإن‬ » ‫حافة‬ ‫الﺴﻘﻒ‬ « ‫فﻲ‬ ‫الصورة‬ ‫هﻲ‬ ‫حدود‬ ‫تتغيﺮ‬ ‫فيها‬ ‫الشدة‬ ‫تدريج‬ ‫ا‬ً‫ي‬ ‫مﻦ‬ ‫ﻗيمة‬ ‫إلى‬ ‫أخﺮى‬ ‫ﻋﻠى‬ ‫مﺴافة‬ ،‫مﻌيﻨة‬ ‫وﻋادة‬ ‫ما‬ ‫تتشﻜل‬ ‫ﻋﻦ‬ ‫طﺮيق‬ ‫تﻘاطﻊ‬ ‫سطحيﻦ‬ . ‫هذا‬ ‫المفه‬ ‫وم‬ ‫مهﻢ‬ ‫فﻲ‬ ‫مهام‬ ‫مﻌالجة‬ ‫الصور‬ ‫مثل‬ ‫اكتشاف‬ ‫الحافة‬ ‫وتجزئة‬ ،‫الصورة‬ ‫خاصة‬ ‫ﻋﻨد‬ ‫التﻌ‬ ‫امل‬ ‫مﻊ‬ ‫الصور‬ ‫التﻲ‬ ‫لها‬ ‫هياكل‬ ‫وميزات‬ ‫مﻌﻘدة‬ . AHMED R. A. SHAMSAN & M. MOHAMADI EDGE DETECTION | LUC01
23 Modeling Intensity Changes (cont’d)  Ridge edge: the image intensity abruptly changes value but then returns to the starting value within some short distance (i.e., usually generated by lines). AHMED R. A. SHAMSAN & M. MOHAMADI EDGE DETECTION | LUC01
Ridge Edge the concept of a “Ridge Edge” in image processing into simple points: 1. Image Intensity: This refers to the brightness or darkness of a pixel in an image. It can vary from low (dark) to high (bright). 2. Edge: In an image, an edge is a boundary between two regions with different intensities. For example, the boundary between a black square and a white background forms an edge. 3. Ridge Edge: This is a type of edge where the intensity changes abruptly from one value to another but then returns to the starting value within some short distance.  Let’s illustrate this with an example: • Imagine a black-and-white image of a line. The line is black, and the background is white. • The edge of this line is a boundary where the intensity changes from white (high intensity) to black (low intensity) and then back to white. • This change in intensity is abrupt, but it doesn’t last. It happens over a short distance, not at a single point. This is what we call a “Ridge Edge”.  In summary, a “Ridge Edge” in an image is a boundary where the intensity changes abruptly from one value to another but then returns to the starting value within some short distance. This concept is crucial in image processing tasks such as edge detection and image segmentation, especially when dealing with images that have line-like structures. ‫ﻣفهﻮم‬ » ‫ريدج‬ ‫إيدج‬ « ‫فﻲ‬ ‫ﻣﻌالجة‬ ‫الصﻮر‬ ‫إلى‬ ‫نقاط‬ ‫بسيطة‬ : • ‫شدة‬ ‫الصﻮرة‬ : ‫يشيﺮ‬ ‫هذا‬ ‫إلى‬ ‫سطوع‬ ‫أو‬ ‫ظﻼم‬ ‫الﺒﻜﺴل‬ ‫فﻲ‬ ‫الصورة‬ . ‫يمﻜﻦ‬ ‫أن‬ ‫يﺨتﻠﻒ‬ ‫مﻦ‬ ‫مﻨﺨ‬ ‫فﺾ‬ ) ‫مﻈﻠﻢ‬ ( ‫إلى‬ ‫مﺮتفﻊ‬ ) ‫مشﺮق‬ ( . • ‫الحافة‬ : ‫فﻲ‬ ،‫الصورة‬ ‫الحافة‬ ‫هﻲ‬ ‫حدود‬ ‫ﺑيﻦ‬ ‫مﻨطﻘتيﻦ‬ ‫ﺑﻜثافة‬ ‫مﺨتﻠفة‬ . ‫ﻋﻠى‬ ‫سﺒيل‬ ‫المث‬ ،‫ال‬ ‫تشﻜل‬ ‫الحدود‬ ‫ﺑيﻦ‬ ‫المﺮﺑﻊ‬ ‫اﻷسود‬ ‫والﺨﻠفية‬ ‫الﺒيﻀاء‬ ‫حافة‬ . • Ridge Edge: ‫هذا‬ ‫ﻧوع‬ ‫مﻦ‬ ‫الحافة‬ ‫حيث‬ ‫تتغيﺮ‬ ‫الشدة‬ ‫فجأة‬ ‫مﻦ‬ ‫ﻗيمة‬ ‫إلى‬ ‫أخﺮى‬ ‫ولﻜﻨها‬ ‫تﻌود‬ ‫ﺑ‬ ‫ﻌد‬ ‫ذلﻚ‬ ‫إلى‬ ‫ﻗيمة‬ ‫الﺒداية‬ ‫ﻋﻠى‬ ‫مﺴافة‬ ‫ﻗصيﺮة‬ . ‫دﻋوﻧا‬ ‫ﻧوﺿح‬ ‫هذا‬ ‫ﺑمثال‬ : • ‫تﺨيل‬ ‫صورة‬ ‫ﺑاﻷﺑيﺾ‬ ‫واﻷسود‬ ‫لﺨﻂ‬ . ‫الﺨﻂ‬ ،‫أسود‬ ‫والﺨﻠفية‬ ‫ﺑيﻀاء‬ . ‫حافة‬ ‫هذا‬ ‫الﺨﻂ‬ ‫هﻲ‬ ‫حدود‬ ‫حيث‬ ‫تتغيﺮ‬ ‫الشدة‬ ‫مﻦ‬ ‫اﻷﺑيﺾ‬ ) ‫ﻋالﻲ‬ ‫الﻜثافة‬ ( ‫إلى‬ ‫اﻷسود‬ ) ‫مﻨﺨفﺾ‬ ‫الﻜثافة‬ ( ‫ثﻢ‬ ‫الﻌودة‬ ‫إلى‬ ‫اﻷﺑيﺾ‬ . ‫هذا‬ ‫التغييﺮ‬ ‫فﻲ‬ ‫الشدة‬ ،‫مفاﺟﺊ‬ ‫لﻜﻨه‬ ‫ﻻ‬ ‫يدوم‬ . ‫يحدث‬ ‫ذلﻚ‬ ‫ﻋﻠى‬ ‫مﺴافة‬ ،‫ﻗصيﺮة‬ ‫وليس‬ ‫فﻲ‬ ‫ﻧﻘ‬ ‫طة‬ ‫واحدة‬ . ‫هذا‬ ‫ما‬ ‫ﻧﺴميه‬ » ‫حافة‬ ‫التﻼل‬ « . • ،‫ﺑاختصار‬ ‫فإن‬ » ‫حافة‬ ‫التﻼل‬ « ‫فﻲ‬ ‫الصورة‬ ‫هﻲ‬ ‫حدود‬ ‫حيث‬ ‫تتغيﺮ‬ ‫الشدة‬ ‫فجأة‬ ‫مﻦ‬ ‫ﻗيمة‬ ‫إل‬ ‫ى‬ ‫أخﺮى‬ ‫ولﻜﻨها‬ ‫تﻌود‬ ‫ﺑﻌد‬ ‫ذلﻚ‬ ‫إلى‬ ‫ﻗيمة‬ ‫الﺒداية‬ ‫ﻋﻠى‬ ‫مﺴافة‬ ‫ﻗصيﺮة‬ . ‫هذا‬ ‫المفهوم‬ ‫مهﻢ‬ ‫فﻲ‬ ‫مهام‬ ‫مﻌالج‬ ‫ة‬ ‫الصور‬ ‫مثل‬ ‫اكتشاف‬ ‫الحافة‬ ‫وتجزئة‬ ،‫الصورة‬ ‫خاصة‬ ‫ﻋﻨد‬ ‫التﻌامل‬ ‫مﻊ‬ ‫الصور‬ ‫التﻲ‬ ‫لها‬ ‫هيا‬ ‫كل‬ ‫تشﺒه‬ ‫الﺨﻂ‬ . EDGE DETECTION | LUC01 AHMED R. A. SHAMSAN & M. MOHAMADI 24

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image processing_ Edge Detection Luc02.pdf

  • 1.
    12 Edge Detection lecture 02 BY AHMED R.A. SHAMSAN MOHAMMED ALMOHAMADI AHMED R. A. SHAMSAN & M. MOHAMADI EDGE DETECTION | LUC01
  • 2.
    13 Edge Descriptors  EdgeDirection:  Specifies the angle or orientation of the edge relative to a reference axis (e.g., horizontal or vertical).  Edge Position:  Indicates the location of the edge within the image (coordinates of the edge pixel).  Edge Strength:  Quantifies the magnitude of the intensity change at the edge. 13 ‫الحافة‬ ‫واصفات‬ ‫اتجاه‬ ‫الحافة‬ : ‫يحدد‬ ‫زاوية‬ ‫أو‬ ‫اتجاه‬ ‫الحافة‬ ‫ﺑالﻨﺴﺒة‬ ‫إلى‬ ‫محور‬ ‫مﺮﺟﻌﻲ‬ ) ‫ﻋﻠى‬ ‫سﺒيل‬ ،‫المثال‬ ‫أف‬ ‫ﻘﻲ‬ ‫أو‬ ‫رأسﻲ‬ ( . ‫ﻣﻮﻗﻊ‬ ‫الحافة‬ : ‫يشيﺮ‬ ‫إلى‬ ‫موﻗﻊ‬ ‫الحافة‬ ‫داخل‬ ‫الصورة‬ ) ‫إحداثيات‬ ‫ﺑﻜﺴل‬ ‫الحافة‬ ( . ‫ﻗﻮة‬ ‫الحافة‬ : ‫يحدد‬ ‫حجﻢ‬ ‫تغيﺮ‬ ‫الشدة‬ ‫ﻋﻨد‬ ‫الحافة‬ . AHMED R. A. SHAMSAN & M. MOHAMADI EDGE DETECTION | LUC01
  • 3.
    Edge Direction the conceptof Edge Direction in the context of image processing. • Edge Direction is a fundamental concept in edge detection algorithms. It refers to the orientation or angle of an edge in an image relative to a reference axis, typically the horizontal or vertical axis. • For instance, consider an image with various shapes like squares, rectangles, and circles. Each shape has edges, and these edges have a specific direction or orientation. This direction is measured as an angle relative to a reference axis. • Here are some examples: • A horizontal edge has a direction of 0 degrees or 180 degrees relative to the vertical axis. • A vertical edge has a direction of 90 degrees or 270 degrees relative to the horizontal axis. • An edge that is diagonal from bottom-left to top-right has a direction of 45 degrees or 225 degrees. • An edge that is diagonal from top-left to bottom-right has a direction of 135 degrees or 315 degrees. • These angles can vary depending on the orientation of the edge. The edge direction is a crucial factor in many image processing tasks, as it helps in identifying and classifying different features in the image. ‫ﻣفهﻮم‬ Edge Direction ‫فﻲ‬ ‫سياق‬ ‫ﻣﻌالجة‬ ‫الصﻮر‬ . ‫هو‬ ‫مفهوم‬ ‫أساسﻲ‬ ‫فﻲ‬ ‫خوارزميات‬ ‫اكتشاف‬ ‫الحافة‬ . ‫يشيﺮ‬ ‫إلى‬ ‫اتجاه‬ ‫أو‬ ‫زاوية‬ ‫الحافة‬ ‫ف‬ ‫ﻲ‬ ‫الصورة‬ ‫ﺑالﻨﺴﺒة‬ ‫إلى‬ ‫المحور‬ ،‫المﺮﺟﻌﻲ‬ ‫وﻋادة‬ ‫ما‬ ‫يﻜون‬ ‫المحور‬ ‫اﻷفﻘﻲ‬ ‫أو‬ ‫الﺮأسﻲ‬ . ‫ﻋﻠى‬ ‫سﺒيل‬ ،‫المثال‬ ‫ﺿﻊ‬ ‫فﻲ‬ ‫اﻋتﺒارك‬ ‫صورة‬ ‫ذات‬ ‫أشﻜال‬ ‫مﺨتﻠفة‬ ‫مثل‬ ‫المﺮﺑﻌات‬ ‫والمﺴتطي‬ ‫ﻼت‬ ‫والدوائﺮ‬ . ‫كل‬ ‫شﻜل‬ ‫له‬ ،‫حواف‬ ‫وهذه‬ ‫الحواف‬ ‫لها‬ ‫اتجاه‬ ‫أو‬ ‫اتجاه‬ ‫محدد‬ . ‫يﻘاس‬ ‫هذا‬ ‫اﻻتجاه‬ ‫كزاوية‬ ‫ﻧﺴﺒ‬ ‫ة‬ ‫إلى‬ ‫المحور‬ ‫المﺮﺟﻌﻲ‬ . ‫فيما‬ ‫يﻠﻲ‬ ‫ﺑﻌﺾ‬ ‫اﻷمثﻠة‬ : • ‫الحافة‬ ‫اﻷفﻘية‬ ‫لها‬ ‫اتجاه‬ 0 ‫درﺟة‬ ‫أو‬ 180 ‫درﺟة‬ ‫ﺑالﻨﺴﺒة‬ ‫لﻠمحور‬ ‫الﺮأسﻲ‬ . • ‫الحافة‬ ‫الﺮأسية‬ ‫لها‬ ‫اتجاه‬ 90 ‫درﺟة‬ ‫أو‬ 270 ‫درﺟة‬ ‫ﺑالﻨﺴﺒة‬ ‫لﻠمحور‬ ‫اﻷفﻘﻲ‬ . • ‫الحافة‬ ‫التﻲ‬ ‫تﻜون‬ ‫ﻗطﺮية‬ ‫مﻦ‬ ‫أسفل‬ ‫اليﺴار‬ ‫إلى‬ ‫أﻋﻠى‬ ‫اليميﻦ‬ ‫لها‬ ‫اتجاه‬ 45 ‫درﺟة‬ ‫أو‬ 225 ‫درﺟة‬ . • ‫الحافة‬ ‫التﻲ‬ ‫تﻜون‬ ‫ﻗطﺮية‬ ‫مﻦ‬ ‫أﻋﻠى‬ ‫اليﺴار‬ ‫إلى‬ ‫أسفل‬ ‫اليميﻦ‬ ‫لها‬ ‫اتجاه‬ 135 ‫درﺟة‬ ‫أو‬ 315 ‫درﺟة‬ . • ‫يمﻜﻦ‬ ‫أن‬ ‫تﺨتﻠﻒ‬ ‫هذه‬ ‫الزوايا‬ ‫ًا‬‫د‬‫اﻋتما‬ ‫ﻋﻠى‬ ‫اتجاه‬ ‫الحافة‬ . ‫يﻌد‬ ‫اتجاه‬ ‫الحافة‬ ً‫ﻼ‬‫ﻋام‬ ‫ا‬ً‫م‬‫حاس‬ ‫ف‬ ‫ﻲ‬ ‫الﻌديد‬ ‫مﻦ‬ ‫مهام‬ ‫مﻌالجة‬ ،‫الصور‬ ‫ﻷﻧه‬ ‫يﺴاﻋد‬ ‫فﻲ‬ ‫تحديد‬ ‫وتصﻨيﻒ‬ ‫الميزات‬ ‫المﺨتﻠفة‬ ‫فﻲ‬ ‫الصورة‬ . EDGE DETECTION | LUC01 AHMED R. A. SHAMSAN & M. MOHAMADI 14
  • 4.
    Edge Position  Insimple terms, Edge Position refers to the specific location of an edge within an image. This location is typically identified by the coordinates of the pixels that make up that edge.  For example, consider an image as a grid of pixels. Each pixel has a unique position, defined by its coordinates (x, y), where x is the horizontal position and y is the vertical position.  When we talk about the “Edge Position”, we are referring to the coordinates of the pixels that form the edge in this grid. These edge pixels are usually where there is a significant change in color or intensity in the image, indicating a boundary or a change in the object within the image.  So, if you have an edge in an image, the “Edge Position” would tell you exactly where that edge is located within the image grid. This is crucial in many image processing tasks, as it helps in identifying and analyzing different objects and features in the image. ‫ﺑﻌﺒارات‬ ،‫ﺑﺴيطة‬ ‫يشيﺮ‬ Edge Position ‫إلى‬ ‫الموﻗﻊ‬ ‫المحدد‬ ‫لﻠحافة‬ ‫داخل‬ ‫الصورة‬ . ‫يتﻢ‬ ‫تحديد‬ ‫هذا‬ ‫الموﻗﻊ‬ ً‫ة‬‫ﻋاد‬ ‫مﻦ‬ ‫خﻼل‬ ‫إحداثيات‬ ‫الﺒﻜﺴﻼت‬ ‫التﻲ‬ ‫تشﻜل‬ ‫تﻠﻚ‬ ‫الحافة‬ . ‫ﻋﻠى‬ ‫سﺒيل‬ ،‫المثال‬ ‫ﺿﻊ‬ ‫فﻲ‬ ‫اﻋتﺒارك‬ ‫الصورة‬ ‫كشﺒﻜة‬ ‫مﻦ‬ ‫الﺒﻜﺴﻼت‬ . ‫كل‬ ‫ﺑﻜﺴل‬ ‫له‬ ‫موﻗﻊ‬ ‫ف‬ ،‫ﺮيد‬ ‫محدد‬ ‫ﺑإحداثياته‬ ) x, y) ، ‫حيث‬ x ‫هو‬ ‫الموﺿﻊ‬ ‫اﻷفﻘﻲ‬ ‫و‬ y ‫هو‬ ‫الموﺿﻊ‬ ‫الﺮأسﻲ‬ . ‫ﻋﻨدما‬ ‫ﻧتحدث‬ ‫ﻋﻦ‬ » ‫موﻗﻊ‬ ‫الحافة‬ « ، ‫فإﻧﻨا‬ ‫ﻧشيﺮ‬ ‫إلى‬ ‫إحداثيات‬ ‫الﺒﻜﺴﻼت‬ ‫التﻲ‬ ‫تشﻜل‬ ‫الحاف‬ ‫ة‬ ‫فﻲ‬ ‫هذه‬ ‫الشﺒﻜة‬ . ‫ﻋادة‬ ‫ما‬ ‫تﻜون‬ ‫هذه‬ ‫الﺒﻜﺴﻼت‬ ‫الحافة‬ ‫حيث‬ ‫يﻜون‬ ‫هﻨاك‬ ‫تغييﺮ‬ ‫كﺒيﺮ‬ ‫فﻲ‬ ‫الﻠون‬ ‫أو‬ ‫الش‬ ‫دة‬ ‫فﻲ‬ ،‫الصورة‬ ‫مما‬ ‫يشيﺮ‬ ‫إلى‬ ‫حد‬ ‫أو‬ ‫تغييﺮ‬ ‫فﻲ‬ ‫الﻜائﻦ‬ ‫داخل‬ ‫الصورة‬ . ،‫لذا‬ ‫إذا‬ ‫كان‬ ‫لديﻚ‬ ‫ميزة‬ ‫فﻲ‬ ،‫الصورة‬ ‫فإن‬ » ‫موﻗﻊ‬ ‫الحافة‬ « ‫سيﺨﺒﺮك‬ ‫ﺑالﻀﺒﻂ‬ ‫ﺑمﻜان‬ ‫وﺟود‬ ‫هذه‬ ‫ا‬ ‫لحافة‬ ‫داخل‬ ‫شﺒﻜة‬ ‫الصور‬ . ‫هذا‬ ‫أمﺮ‬ ‫ﺑالﻎ‬ ‫اﻷهمية‬ ‫فﻲ‬ ‫الﻌديد‬ ‫مﻦ‬ ‫مهام‬ ‫مﻌالجة‬ ،‫الصور‬ ‫ﻷﻧه‬ ‫يﺴاﻋد‬ ‫فﻲ‬ ‫تح‬ ‫ديد‬ ‫وتحﻠيل‬ ‫اﻷشياء‬ ‫والميزات‬ ‫المﺨتﻠفة‬ ‫فﻲ‬ ‫الصورة‬ . EDGE DETECTION | LUC01 AHMED R. A. SHAMSAN & M. MOHAMADI 15
  • 5.
    Edge Strength  theconcept of Edge Strength in image processing.  In simple terms, Edge Strength is a measure of how “sharp” or “strong” an edge is in an image. It quantifies the magnitude of the change in intensity at the edge.  Imagine you’re looking at a black-and-white image. The intensity of each pixel in the image is represented by a grayscale value, with black being the lowest intensity and white being the highest. Now, if you have an edge in the image, this edge is usually where there is a significant change in these grayscale values - that is, a change from a darker area (lower intensity) to a lighter area (higher intensity), or vice versa.  The Edge Strength is a measure of how big this change in intensity is. If the change is very sudden and large (for example, a transition from black to white), the edge is considered “strong” and will have a high Edge Strength value. On the other hand, if the change is gradual or small (for example, a transition from dark gray to light gray), the edge is considered “weak” and will have a low Edge Strength value.  This concept is crucial in many image processing tasks, as it helps in identifying and distinguishing different features in the image based on the sharpness or strength of their edges. ‫الصور‬ ‫معالجة‬ ‫في‬ ‫الحافة‬ ‫قوة‬ ‫مفهوم‬ . ‫ﺑﻌﺒارات‬ ،‫ﺑﺴيطة‬ Edge Strength ‫هو‬ ‫مﻘياس‬ ‫لمدى‬ ‫وﺟود‬ ‫حافة‬ » ‫حادة‬ « ‫أو‬ » ‫ﻗوية‬ « ‫فﻲ‬ ‫الصورة‬ . ‫إﻧه‬ ‫يحدد‬ ‫حجﻢ‬ ‫التغيﺮ‬ ‫فﻲ‬ ‫الشدة‬ ‫ﻋﻨد‬ ‫الحافة‬ . ‫تﺨيل‬ ‫أﻧﻚ‬ ‫تﻨﻈﺮ‬ ‫إلى‬ ‫صورة‬ ‫ﺑاﻷﺑيﺾ‬ ‫واﻷسود‬ . ‫يتﻢ‬ ‫تمثيل‬ ‫شدة‬ ‫كل‬ ‫ﺑﻜﺴل‬ ‫فﻲ‬ ‫الص‬ ‫ورة‬ ‫ﺑﻘيمة‬ ،‫رمادية‬ ‫حيث‬ ‫يﻜون‬ ‫الﻠون‬ ‫اﻷسود‬ ‫هو‬ ‫اﻷﻗل‬ ‫شدة‬ ‫واﻷﺑيﺾ‬ ‫هو‬ ‫اﻷﻋﻠى‬ . ،‫اﻵن‬ ‫إذا‬ ‫كان‬ ‫لديﻚ‬ ‫ميزة‬ ‫فﻲ‬ ،‫الصورة‬ ‫فهذه‬ ‫الحافة‬ ‫ﻋادة‬ ‫ما‬ ‫تﻜون‬ ‫حيث‬ ‫يوﺟد‬ ‫تغييﺮ‬ ‫كﺒيﺮ‬ ‫فﻲ‬ ‫هذه‬ ‫الﻘيﻢ‬ ‫الﺮمادية‬ - ‫أي‬ ‫تغييﺮ‬ ‫مﻦ‬ ‫مﻨطﻘة‬ ‫أكثﺮ‬ ‫ﻗتامة‬ ) ‫شدة‬ ‫أﻗل‬ ( ‫إلى‬ ‫مﻨطﻘة‬ ‫أخﻒ‬ ) ‫كثافة‬ ‫أﻋﻠى‬ ( ، ‫أو‬ ‫الﻌﻜس‬ . ‫ﻗوة‬ ‫الحافة‬ ‫هﻲ‬ ‫مﻘياس‬ ‫لحجﻢ‬ ‫هذا‬ ‫التغييﺮ‬ ‫فﻲ‬ ‫الشدة‬ . ‫إذا‬ ‫كان‬ ‫التغييﺮ‬ ‫ا‬ً‫ﺌ‬‫مفاﺟ‬ ‫وكﺒي‬ ‫ا‬ً‫ﺮ‬ ‫ًا‬‫د‬‫ﺟ‬ ) ‫ﻋﻠى‬ ‫سﺒيل‬ ،‫المثال‬ ‫اﻻﻧتﻘال‬ ‫مﻦ‬ ‫اﻷسود‬ ‫إلى‬ ‫اﻷﺑيﺾ‬ ( ، ‫فإن‬ ‫الحافة‬ ‫تﻌتﺒﺮ‬ » ‫ﻗوية‬ « ‫وست‬ ‫ﻜون‬ ‫لها‬ ‫ﻗيمة‬ ‫ﻋالية‬ ‫لﻘوة‬ ‫الحافة‬ . ‫مﻦ‬ ‫ﻧاحية‬ ،‫أخﺮى‬ ‫إذا‬ ‫كان‬ ‫التغييﺮ‬ ‫ا‬ً‫ي‬‫تدريج‬ ‫أو‬ ‫ا‬ً‫صغيﺮ‬ ) ‫ﻋﻠى‬ ‫س‬ ‫ﺒيل‬ ،‫المثال‬ ‫اﻻﻧتﻘال‬ ‫مﻦ‬ ‫الﺮمادي‬ ‫الداكﻦ‬ ‫إلى‬ ‫الﺮمادي‬ ‫الفاتح‬ ( ، ‫فإن‬ ‫الحافة‬ ‫تﻌتﺒﺮ‬ » ‫ﺿﻌيفة‬ « ‫وس‬ ‫تﻜون‬ ‫لها‬ ‫ﻗيمة‬ ‫مﻨﺨفﻀة‬ ‫لﻘوة‬ ‫الحافة‬ . ‫هذا‬ ‫المفهوم‬ ‫حاسﻢ‬ ‫فﻲ‬ ‫الﻌديد‬ ‫مﻦ‬ ‫مهام‬ ‫مﻌالجة‬ ،‫الصور‬ ‫ﻷﻧه‬ ‫يﺴاﻋد‬ ‫فﻲ‬ ‫تحديد‬ ‫وتمييز‬ ‫ال‬ ‫ميزات‬ ‫المﺨتﻠفة‬ ‫فﻲ‬ ‫الصورة‬ ً‫ء‬‫ﺑﻨا‬ ‫ﻋﻠى‬ ‫حدة‬ ‫أو‬ ‫ﻗوة‬ ‫حوافها‬ . EDGE DETECTION | LUC01 AHMED R. A. SHAMSAN & M. MOHAMADI 16
  • 6.
    17 Modeling Intensity Changes Step edge: the image intensity abruptly changes from one value on one side of the discontinuity to a different value on the opposite side. ‫النمذجة‬ ‫شدة‬ ‫تغييرات‬ ‫ﺣافة‬ ‫الخطﻮة‬ : ‫تتغيﺮ‬ ‫شدة‬ ‫الصورة‬ ‫فجأة‬ ‫مﻦ‬ ‫ﻗيمة‬ ‫واحدة‬ ‫ﻋﻠى‬ ‫ﺟاﻧﺐ‬ ‫واحد‬ ‫مﻦ‬ ‫اﻻﻧﻘطاع‬ ‫إل‬ ‫ى‬ ‫ﻗيمة‬ ‫مﺨتﻠفة‬ ‫ﻋﻠى‬ ‫الجاﻧﺐ‬ ‫اﻵخﺮ‬ . AHMED R. A. SHAMSAN & M. MOHAMADI EDGE DETECTION | LUC01
  • 7.
    18 Step edge  theconcept of a “Step Edge” in image processing into simple points:  Image Intensity: This refers to the brightness or darkness of a pixel in an image. It can vary from low (dark) to high (bright).  Edge: In an image, an edge is a boundary between two regions with different intensities. For example, the boundary between a black square and a white background forms an edge.  Step Edge: This is a type of edge where the intensity changes abruptly from one side to the other.  Let’s illustrate this with an example:  Imagine a black-and-white image of a square. The square is black, and the background is white.  The edge of the square is a boundary where the intensity changes from black (low intensity) to white (high intensity).  This change in intensity is abrupt, meaning it happens suddenly. On one side of the edge, you have the black square (low intensity), and on the other side, you have the white background (high intensity).  This sudden change in intensity is what we call a “Step Edge”.  In summary, a “Step Edge” in an image is a boundary where the intensity changes suddenly from one value to another. ‫مفهوم‬ » ‫حافة‬ ‫الﺨطوة‬ « ‫فﻲ‬ ‫مﻌالجة‬ ‫الصور‬ ‫إلى‬ ‫ﻧﻘاط‬ ‫ﺑﺴيطة‬ : • ‫شدة‬ ‫الصﻮرة‬ : ‫يشيﺮ‬ ‫هذا‬ ‫إلى‬ ‫سطوع‬ ‫أو‬ ‫ظﻼم‬ ‫الﺒﻜﺴل‬ ‫فﻲ‬ ‫الصورة‬ . ‫يمﻜﻦ‬ ‫أن‬ ‫يﺨتﻠﻒ‬ ‫مﻦ‬ ‫مﻨﺨ‬ ‫فﺾ‬ ) ‫مﻈﻠﻢ‬ ( ‫إلى‬ ‫مﺮتفﻊ‬ ) ‫مشﺮق‬ ( . • ‫الحافة‬ : ‫فﻲ‬ ،‫الصورة‬ ‫الحافة‬ ‫هﻲ‬ ‫حدود‬ ‫ﺑيﻦ‬ ‫مﻨطﻘتيﻦ‬ ‫ﺑﻜثافة‬ ‫مﺨتﻠفة‬ . ‫ﻋﻠى‬ ‫سﺒيل‬ ‫المث‬ ،‫ال‬ ‫تشﻜل‬ ‫الحدود‬ ‫ﺑيﻦ‬ ‫المﺮﺑﻊ‬ ‫اﻷسود‬ ‫والﺨﻠفية‬ ‫الﺒيﻀاء‬ ‫حافة‬ . • Step Edge: ‫هذا‬ ‫ﻧوع‬ ‫مﻦ‬ ‫الحافة‬ ‫حيث‬ ‫تتغيﺮ‬ ‫الشدة‬ ‫فجأة‬ ‫مﻦ‬ ‫ﺟاﻧﺐ‬ ‫إلى‬ ‫آخﺮ‬ . ‫دﻋوﻧا‬ ‫ﻧوﺿح‬ ‫هذا‬ ‫ﺑمثال‬ : • ‫تﺨيل‬ ‫صورة‬ ‫ﺑاﻷﺑيﺾ‬ ‫واﻷسود‬ ‫لمﺮﺑﻊ‬ . ‫المﺮﺑﻊ‬ ،‫أسود‬ ‫والﺨﻠفية‬ ‫ﺑيﻀاء‬ . • ‫حافة‬ ‫المﺮﺑﻊ‬ ‫هﻲ‬ ‫حدود‬ ‫حيث‬ ‫تتغيﺮ‬ ‫الشدة‬ ‫مﻦ‬ ‫اﻷسود‬ ) ‫مﻨﺨفﺾ‬ ‫الﻜثافة‬ ( ‫إلى‬ ‫اﻷﺑيﺾ‬ ) ‫ﻋا‬ ‫لﻲ‬ ‫الﻜثافة‬ ( . • ‫هذا‬ ‫التغييﺮ‬ ‫فﻲ‬ ‫الشدة‬ ،‫مفاﺟﺊ‬ ‫مما‬ ‫يﻌﻨﻲ‬ ‫أﻧه‬ ‫يحدث‬ ‫فجأة‬ . ‫ﻋﻠى‬ ‫ﺟاﻧﺐ‬ ‫واحد‬ ‫مﻦ‬ ،‫الحافة‬ ‫لديﻚ‬ ‫المﺮﺑﻊ‬ ‫اﻷسود‬ ) ‫كثافة‬ ‫مﻨﺨفﻀة‬ ( ، ‫وﻋﻠى‬ ‫الجاﻧﺐ‬ ،‫اﻵخﺮ‬ ‫لديﻚ‬ ‫الﺨﻠفية‬ ‫الﺒيﻀاء‬ ) ‫كثافة‬ ‫ﻋالية‬ ( . • ‫هذا‬ ‫التغييﺮ‬ ‫المفاﺟﺊ‬ ‫فﻲ‬ ‫الشدة‬ ‫هو‬ ‫ما‬ ‫ﻧﺴميه‬ » Step Edge». • ،‫ﺑاختصار‬ ‫فإن‬ » Step Edge» ‫فﻲ‬ ‫الصورة‬ ‫هﻲ‬ ‫حدود‬ ‫تتغيﺮ‬ ‫فيها‬ ‫الشدة‬ ‫فجأة‬ ‫مﻦ‬ ‫ﻗيمة‬ ‫إلى‬ ‫أخﺮ‬ ‫ى‬ . AHMED R. A. SHAMSAN & M. MOHAMADI EDGE DETECTION | LUC01
  • 8.
    19 Modeling Intensity Changes(contd)  Ramp edge:  a step edge where the intensity change is not instantaneous but occurs over a finite distance. ‫النمذجة‬ ‫شدة‬ ‫تغييرات‬ ‫المنحدر‬ ‫ﺣافة‬ : ‫مح‬ ‫مﺴافة‬ ‫ﻋﻠى‬ ‫يحدث‬ ‫ولﻜﻨه‬ ‫ا‬ً‫ي‬‫فور‬ ‫ليس‬ ‫الشدة‬ ‫تغيﺮ‬ ‫حيث‬ ‫خطوة‬ ‫حافة‬ ‫دودة‬ AHMED R. A. SHAMSAN & M. MOHAMADI EDGE DETECTION | LUC01
  • 9.
    Ramp edge  theconcept of a “Ramp Edge” in image processing into simple points: 1. Image Intensity: This refers to the brightness or darkness of a pixel in an image. It can vary from low (dark) to high (bright). 2. Edge: In an image, an edge is a boundary between two regions with different intensities. For example, the boundary between a black square and a white background forms an edge. 3. Step Edge: This is a type of edge where the intensity changes abruptly from one side to the other. 4. Ramp Edge: Unlike a step edge, a ramp edge is where the intensity change is not instantaneous but occurs over a finite distance.  Let’s illustrate this with an example: • Imagine a black-and-white image of a gradient. The gradient transitions from black to white. • The edge of this gradient is a boundary where the intensity changes from black (low intensity) to white (high intensity). • However, this change in intensity is not abrupt, but gradual. It happens over a distance, not at a single point. This is what we call a “Ramp Edge”.  In summary, a “Ramp Edge” in an image is a boundary where the intensity changes gradually from one value to another over a certain distance. This concept is crucial in image processing tasks such as edge detection and image segmentation, especially when dealing with images that have gradual transitions in intensity. ‫ﻣفهﻮم‬ » ‫ﺣافة‬ ‫المنحدر‬ « ‫فﻲ‬ ‫ﻣﻌالجة‬ ‫الصﻮر‬ ‫إلى‬ ‫نقاط‬ ‫بسيطة‬ : • ‫شدة‬ ‫الصﻮرة‬ : ‫يشيﺮ‬ ‫هذا‬ ‫إلى‬ ‫سطوع‬ ‫أو‬ ‫ظﻼم‬ ‫الﺒﻜﺴل‬ ‫فﻲ‬ ‫الصورة‬ . ‫يمﻜﻦ‬ ‫أن‬ ‫يﺨتﻠﻒ‬ ‫مﻦ‬ ‫مﻨﺨ‬ ‫فﺾ‬ ) ‫مﻈﻠﻢ‬ ( ‫إلى‬ ‫مﺮتفﻊ‬ ) ‫مشﺮق‬ ( . • ‫الحافة‬ : ‫فﻲ‬ ،‫الصورة‬ ‫الحافة‬ ‫هﻲ‬ ‫حدود‬ ‫ﺑيﻦ‬ ‫مﻨطﻘتيﻦ‬ ‫ﺑﻜثافة‬ ‫مﺨتﻠفة‬ . ‫ﻋﻠى‬ ‫سﺒيل‬ ‫المث‬ ،‫ال‬ ‫تشﻜل‬ ‫الحدود‬ ‫ﺑيﻦ‬ ‫المﺮﺑﻊ‬ ‫اﻷسود‬ ‫والﺨﻠفية‬ ‫الﺒيﻀاء‬ ‫حافة‬ . • Step Edge: ‫هذا‬ ‫ﻧوع‬ ‫مﻦ‬ ‫الحافة‬ ‫حيث‬ ‫تتغيﺮ‬ ‫الشدة‬ ‫فجأة‬ ‫مﻦ‬ ‫ﺟاﻧﺐ‬ ‫إلى‬ ‫آخﺮ‬ . • ‫ﺣافة‬ ‫المنحدر‬ : ‫ﻋﻠى‬ ‫ﻋﻜس‬ ‫حافة‬ ،‫الﺨطوة‬ ‫فإن‬ ‫حافة‬ ‫المﻨحدر‬ ‫هﻲ‬ ‫المﻜان‬ ‫الذي‬ ‫ﻻ‬ ‫يﻜون‬ ‫فيه‬ ‫تغ‬ ‫ييﺮ‬ ‫الشدة‬ ‫ا‬ً‫ي‬‫فور‬ ‫ولﻜﻨه‬ ‫يحدث‬ ‫ﻋﻠى‬ ‫مﺴافة‬ ‫محدودة‬ . ‫دﻋوﻧا‬ ‫ﻧوﺿح‬ ‫هذا‬ ‫ﺑمثال‬ : • ‫تﺨيل‬ ‫صورة‬ ‫ﺑاﻷﺑيﺾ‬ ‫واﻷسود‬ ‫لﻠتدرج‬ . ‫يﻨتﻘل‬ ‫التدرج‬ ‫مﻦ‬ ‫اﻷسود‬ ‫إلى‬ ‫اﻷﺑيﺾ‬ . • ‫حافة‬ ‫هذا‬ ‫التدرج‬ ‫هﻲ‬ ‫حدود‬ ‫حيث‬ ‫تتغيﺮ‬ ‫الشدة‬ ‫مﻦ‬ ‫اﻷسود‬ ) ‫مﻨﺨفﺾ‬ ‫الﻜثافة‬ ( ‫إلى‬ ‫اﻷ‬ ‫ﺑيﺾ‬ ) ‫ﻋالﻲ‬ ‫الﻜثافة‬ ( . ‫ومﻊ‬ ،‫ذلﻚ‬ ‫فإن‬ ‫هذا‬ ‫التغييﺮ‬ ‫فﻲ‬ ‫الشدة‬ ‫ليس‬ ،‫ا‬ً‫ﺌ‬‫مفاﺟ‬ ‫ولﻜﻨه‬ ‫تدريجﻲ‬ . ‫يحدث‬ ‫ذلﻚ‬ ‫ﻋ‬ ‫ﻠى‬ ،‫مﺴافة‬ ‫وليس‬ ‫فﻲ‬ ‫ﻧﻘطة‬ ‫واحدة‬ . ‫هذا‬ ‫ما‬ ‫ﻧﺴميه‬ » ‫حافة‬ ‫المﻨحدر‬ « . • ،‫ﺑاختصار‬ ‫فإن‬ » ‫حافة‬ ‫المﻨحدر‬ « ‫فﻲ‬ ‫الصورة‬ ‫هﻲ‬ ‫حدود‬ ‫تتغيﺮ‬ ‫فيها‬ ‫الشدة‬ ‫تدريج‬ ‫ا‬ً‫ي‬ ‫مﻦ‬ ‫ﻗيمة‬ ‫إلى‬ ‫أخﺮى‬ ‫ﻋﻠى‬ ‫مﺴافة‬ ‫مﻌيﻨة‬ . ‫هذا‬ ‫المفهوم‬ ‫حاسﻢ‬ ‫فﻲ‬ ‫مهام‬ ‫مﻌالجة‬ ‫الصور‬ ‫مثل‬ ‫اكتشاف‬ ‫الحافة‬ ‫وتجزئة‬ ،‫الصورة‬ ‫خاصة‬ ‫ﻋﻨد‬ ‫التﻌامل‬ ‫مﻊ‬ ‫الصور‬ ‫التﻲ‬ ‫لها‬ ‫اﻧتﻘاﻻ‬ ‫ت‬ ‫تدريجية‬ ‫فﻲ‬ ‫الشدة‬ . EDGE DETECTION | LUC01 AHMED R. A. SHAMSAN & M. MOHAMADI 20
  • 10.
    21 Modeling Intensity Changes(contd)  Roof edge: a ridge edge where the intensity change is not instantaneous but occurs over a finite distance (i.e., usually generated by the intersection of two surfaces). ‫السقف‬ ‫ﺣافة‬ : ‫محدودة‬ ‫مﺴافة‬ ‫ﻋﻠى‬ ‫يحدث‬ ‫ولﻜﻨه‬ ‫ا‬ً‫ي‬‫فور‬ ‫الشدة‬ ‫تغييﺮ‬ ‫يﻜون‬ ‫ﻻ‬ ‫حيث‬ ‫التﻼل‬ ‫حافة‬ ) ‫إﻧ‬ ‫يتﻢ‬ ‫ما‬ ‫ﻋادة‬ ‫أي‬ ‫ﻋﻦ‬ ‫شاؤه‬ ‫سطحيﻦ‬ ‫تﻘاطﻊ‬ ‫طﺮيق‬ .( AHMED R. A. SHAMSAN & M. MOHAMADI EDGE DETECTION | LUC01
  • 11.
    22 Roof edge  theconcept of a “Roof Edge” in image processing into simple points: 1. Image Intensity: This refers to the brightness or darkness of a pixel in an image. It can vary from low (dark) to high (bright). 2. Edge: In an image, an edge is a boundary between two regions with different intensities. For example, the boundary between a black square and a white background forms an edge. 3. Ridge Edge: This is a type of edge where the intensity changes gradually from one side to the other, similar to a ramp edge. 4. Roof Edge: A roof edge is a special type of ridge edge. It is usually formed by the intersection of two surfaces. The intensity change is not instantaneous but occurs over a finite distance.  Let’s illustrate this with an example: • Imagine a black-and-white image of a pyramid. The edges of the pyramid are formed by the intersection of two surfaces. • The edge of this pyramid is a boundary where the intensity changes from black (low intensity) to white (high intensity). • However, this change in intensity is not abrupt, but gradual. It happens over a distance, not at a single point. This is what we call a “Roof Edge”.  In summary, a “Roof Edge” in an image is a boundary where the intensity changes gradually from one value to another over a certain distance, typically formed by the intersection of two surfaces. This concept is crucial in image processing tasks such as edge detection and image segmentation, especially when dealing with images that have complex structures and features. ‫ﻣفهﻮم‬ » ‫ﺣافة‬ ‫السقف‬ « ‫فﻲ‬ ‫ﻣﻌالجة‬ ‫الصﻮر‬ ‫إلى‬ ‫نقاط‬ ‫بسيطة‬ : • ‫شدة‬ ‫الصﻮرة‬ : ‫يشيﺮ‬ ‫هذا‬ ‫إلى‬ ‫سطوع‬ ‫أو‬ ‫ظﻼم‬ ‫الﺒﻜﺴل‬ ‫فﻲ‬ ‫الصورة‬ . ‫يمﻜﻦ‬ ‫أن‬ ‫يﺨتﻠﻒ‬ ‫مﻦ‬ ‫مﻨﺨ‬ ‫فﺾ‬ ) ‫مﻈﻠﻢ‬ ( ‫إلى‬ ‫مﺮتفﻊ‬ ) ‫مشﺮق‬ ( . • ‫الحافة‬ : ‫فﻲ‬ ،‫الصورة‬ ‫الحافة‬ ‫هﻲ‬ ‫حدود‬ ‫ﺑيﻦ‬ ‫مﻨطﻘتيﻦ‬ ‫ﺑﻜثافة‬ ‫مﺨتﻠفة‬ . ‫ﻋﻠى‬ ‫سﺒيل‬ ‫المث‬ ،‫ال‬ ‫تشﻜل‬ ‫الحدود‬ ‫ﺑيﻦ‬ ‫المﺮﺑﻊ‬ ‫اﻷسود‬ ‫والﺨﻠفية‬ ‫الﺒيﻀاء‬ ‫حافة‬ . • ‫ﺣافة‬ ‫التﻼل‬ : ‫هذا‬ ‫ﻧوع‬ ‫مﻦ‬ ‫الحافة‬ ‫حيث‬ ‫تتغيﺮ‬ ‫الشدة‬ ‫ا‬ً‫ي‬‫تدريج‬ ‫مﻦ‬ ‫ﺟاﻧﺐ‬ ‫إلى‬ ،‫آخﺮ‬ ‫ﻋﻠى‬ ‫غﺮا‬ ‫ر‬ ‫حافة‬ ‫المﻨحدر‬ . • ‫ﺣافة‬ ‫السقف‬ : ‫حافة‬ ‫الﺴﻘﻒ‬ ‫هﻲ‬ ‫ﻧوع‬ ‫خاص‬ ‫مﻦ‬ ‫حافة‬ ‫التﻼل‬ . ‫يتﻜون‬ ‫ﻋادة‬ ‫مﻦ‬ ‫تﻘاطﻊ‬ ‫سطحيﻦ‬ . ‫تغييﺮ‬ ‫الشدة‬ ‫ليس‬ ‫ا‬ً‫ي‬‫فور‬ ‫ولﻜﻨه‬ ‫يحدث‬ ‫ﻋﻠى‬ ‫مﺴافة‬ ‫محدودة‬ . ‫دﻋوﻧا‬ ‫ﻧوﺿح‬ ‫هذا‬ ‫ﺑمثال‬ : • ‫تﺨيل‬ ‫صورة‬ ‫ﺑاﻷﺑيﺾ‬ ‫واﻷسود‬ ‫لهﺮم‬ . ‫تتشﻜل‬ ‫حواف‬ ‫الهﺮم‬ ‫ﻋﻦ‬ ‫طﺮيق‬ ‫تﻘاطﻊ‬ ‫سطح‬ ‫يﻦ‬ . ‫حافة‬ ‫هذا‬ ‫الهﺮم‬ ‫هﻲ‬ ‫حدود‬ ‫حيث‬ ‫تتغيﺮ‬ ‫الشدة‬ ‫مﻦ‬ ‫اﻷسود‬ ) ‫مﻨﺨفﺾ‬ ‫الﻜثافة‬ ( ‫إلى‬ ‫اﻷﺑ‬ ‫يﺾ‬ ) ‫ﻋالﻲ‬ ‫الﻜثافة‬ ( . ‫ومﻊ‬ ،‫ذلﻚ‬ ‫فإن‬ ‫هذا‬ ‫التغييﺮ‬ ‫فﻲ‬ ‫الشدة‬ ‫ليس‬ ،‫ا‬ً‫ﺌ‬‫مفاﺟ‬ ‫ولﻜﻨه‬ ‫تدريجﻲ‬ . ‫يحدث‬ ‫ذلﻚ‬ ‫ﻋﻠى‬ ،‫مﺴافة‬ ‫وليس‬ ‫فﻲ‬ ‫ﻧﻘطة‬ ‫واحدة‬ . ‫هذا‬ ‫ما‬ ‫ﻧﺴميه‬ » ‫حافة‬ ‫الﺴﻘﻒ‬ « . • ،‫ﺑاختصار‬ ‫فإن‬ » ‫حافة‬ ‫الﺴﻘﻒ‬ « ‫فﻲ‬ ‫الصورة‬ ‫هﻲ‬ ‫حدود‬ ‫تتغيﺮ‬ ‫فيها‬ ‫الشدة‬ ‫تدريج‬ ‫ا‬ً‫ي‬ ‫مﻦ‬ ‫ﻗيمة‬ ‫إلى‬ ‫أخﺮى‬ ‫ﻋﻠى‬ ‫مﺴافة‬ ،‫مﻌيﻨة‬ ‫وﻋادة‬ ‫ما‬ ‫تتشﻜل‬ ‫ﻋﻦ‬ ‫طﺮيق‬ ‫تﻘاطﻊ‬ ‫سطحيﻦ‬ . ‫هذا‬ ‫المفه‬ ‫وم‬ ‫مهﻢ‬ ‫فﻲ‬ ‫مهام‬ ‫مﻌالجة‬ ‫الصور‬ ‫مثل‬ ‫اكتشاف‬ ‫الحافة‬ ‫وتجزئة‬ ،‫الصورة‬ ‫خاصة‬ ‫ﻋﻨد‬ ‫التﻌ‬ ‫امل‬ ‫مﻊ‬ ‫الصور‬ ‫التﻲ‬ ‫لها‬ ‫هياكل‬ ‫وميزات‬ ‫مﻌﻘدة‬ . AHMED R. A. SHAMSAN & M. MOHAMADI EDGE DETECTION | LUC01
  • 12.
    23 Modeling Intensity Changes(cont’d)  Ridge edge: the image intensity abruptly changes value but then returns to the starting value within some short distance (i.e., usually generated by lines). AHMED R. A. SHAMSAN & M. MOHAMADI EDGE DETECTION | LUC01
  • 13.
    Ridge Edge the conceptof a “Ridge Edge” in image processing into simple points: 1. Image Intensity: This refers to the brightness or darkness of a pixel in an image. It can vary from low (dark) to high (bright). 2. Edge: In an image, an edge is a boundary between two regions with different intensities. For example, the boundary between a black square and a white background forms an edge. 3. Ridge Edge: This is a type of edge where the intensity changes abruptly from one value to another but then returns to the starting value within some short distance.  Let’s illustrate this with an example: • Imagine a black-and-white image of a line. The line is black, and the background is white. • The edge of this line is a boundary where the intensity changes from white (high intensity) to black (low intensity) and then back to white. • This change in intensity is abrupt, but it doesn’t last. It happens over a short distance, not at a single point. This is what we call a “Ridge Edge”.  In summary, a “Ridge Edge” in an image is a boundary where the intensity changes abruptly from one value to another but then returns to the starting value within some short distance. This concept is crucial in image processing tasks such as edge detection and image segmentation, especially when dealing with images that have line-like structures. ‫ﻣفهﻮم‬ » ‫ريدج‬ ‫إيدج‬ « ‫فﻲ‬ ‫ﻣﻌالجة‬ ‫الصﻮر‬ ‫إلى‬ ‫نقاط‬ ‫بسيطة‬ : • ‫شدة‬ ‫الصﻮرة‬ : ‫يشيﺮ‬ ‫هذا‬ ‫إلى‬ ‫سطوع‬ ‫أو‬ ‫ظﻼم‬ ‫الﺒﻜﺴل‬ ‫فﻲ‬ ‫الصورة‬ . ‫يمﻜﻦ‬ ‫أن‬ ‫يﺨتﻠﻒ‬ ‫مﻦ‬ ‫مﻨﺨ‬ ‫فﺾ‬ ) ‫مﻈﻠﻢ‬ ( ‫إلى‬ ‫مﺮتفﻊ‬ ) ‫مشﺮق‬ ( . • ‫الحافة‬ : ‫فﻲ‬ ،‫الصورة‬ ‫الحافة‬ ‫هﻲ‬ ‫حدود‬ ‫ﺑيﻦ‬ ‫مﻨطﻘتيﻦ‬ ‫ﺑﻜثافة‬ ‫مﺨتﻠفة‬ . ‫ﻋﻠى‬ ‫سﺒيل‬ ‫المث‬ ،‫ال‬ ‫تشﻜل‬ ‫الحدود‬ ‫ﺑيﻦ‬ ‫المﺮﺑﻊ‬ ‫اﻷسود‬ ‫والﺨﻠفية‬ ‫الﺒيﻀاء‬ ‫حافة‬ . • Ridge Edge: ‫هذا‬ ‫ﻧوع‬ ‫مﻦ‬ ‫الحافة‬ ‫حيث‬ ‫تتغيﺮ‬ ‫الشدة‬ ‫فجأة‬ ‫مﻦ‬ ‫ﻗيمة‬ ‫إلى‬ ‫أخﺮى‬ ‫ولﻜﻨها‬ ‫تﻌود‬ ‫ﺑ‬ ‫ﻌد‬ ‫ذلﻚ‬ ‫إلى‬ ‫ﻗيمة‬ ‫الﺒداية‬ ‫ﻋﻠى‬ ‫مﺴافة‬ ‫ﻗصيﺮة‬ . ‫دﻋوﻧا‬ ‫ﻧوﺿح‬ ‫هذا‬ ‫ﺑمثال‬ : • ‫تﺨيل‬ ‫صورة‬ ‫ﺑاﻷﺑيﺾ‬ ‫واﻷسود‬ ‫لﺨﻂ‬ . ‫الﺨﻂ‬ ،‫أسود‬ ‫والﺨﻠفية‬ ‫ﺑيﻀاء‬ . ‫حافة‬ ‫هذا‬ ‫الﺨﻂ‬ ‫هﻲ‬ ‫حدود‬ ‫حيث‬ ‫تتغيﺮ‬ ‫الشدة‬ ‫مﻦ‬ ‫اﻷﺑيﺾ‬ ) ‫ﻋالﻲ‬ ‫الﻜثافة‬ ( ‫إلى‬ ‫اﻷسود‬ ) ‫مﻨﺨفﺾ‬ ‫الﻜثافة‬ ( ‫ثﻢ‬ ‫الﻌودة‬ ‫إلى‬ ‫اﻷﺑيﺾ‬ . ‫هذا‬ ‫التغييﺮ‬ ‫فﻲ‬ ‫الشدة‬ ،‫مفاﺟﺊ‬ ‫لﻜﻨه‬ ‫ﻻ‬ ‫يدوم‬ . ‫يحدث‬ ‫ذلﻚ‬ ‫ﻋﻠى‬ ‫مﺴافة‬ ،‫ﻗصيﺮة‬ ‫وليس‬ ‫فﻲ‬ ‫ﻧﻘ‬ ‫طة‬ ‫واحدة‬ . ‫هذا‬ ‫ما‬ ‫ﻧﺴميه‬ » ‫حافة‬ ‫التﻼل‬ « . • ،‫ﺑاختصار‬ ‫فإن‬ » ‫حافة‬ ‫التﻼل‬ « ‫فﻲ‬ ‫الصورة‬ ‫هﻲ‬ ‫حدود‬ ‫حيث‬ ‫تتغيﺮ‬ ‫الشدة‬ ‫فجأة‬ ‫مﻦ‬ ‫ﻗيمة‬ ‫إل‬ ‫ى‬ ‫أخﺮى‬ ‫ولﻜﻨها‬ ‫تﻌود‬ ‫ﺑﻌد‬ ‫ذلﻚ‬ ‫إلى‬ ‫ﻗيمة‬ ‫الﺒداية‬ ‫ﻋﻠى‬ ‫مﺴافة‬ ‫ﻗصيﺮة‬ . ‫هذا‬ ‫المفهوم‬ ‫مهﻢ‬ ‫فﻲ‬ ‫مهام‬ ‫مﻌالج‬ ‫ة‬ ‫الصور‬ ‫مثل‬ ‫اكتشاف‬ ‫الحافة‬ ‫وتجزئة‬ ،‫الصورة‬ ‫خاصة‬ ‫ﻋﻨد‬ ‫التﻌامل‬ ‫مﻊ‬ ‫الصور‬ ‫التﻲ‬ ‫لها‬ ‫هيا‬ ‫كل‬ ‫تشﺒه‬ ‫الﺨﻂ‬ . EDGE DETECTION | LUC01 AHMED R. A. SHAMSAN & M. MOHAMADI 24