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TRAITEMENT des
IMAGES MEDICALES
MASTER PhyMed
GMPH308 - Physique de l’imagerie médicale
Fayçal Ben Bouallè[email protected]://scinti.edu.umontpellier.fr
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𝑓 𝑥, 𝑦 : ℝ2 → Ω (ℝ,ℝ+, ℕ) 𝑓 𝑖, 𝑗 : … → …
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N
N
𝑓 𝑖, 𝑗 : 1: N × 1: N → …
𝑥, 𝑦 → 𝑖, 𝑗 ∶ 𝑥𝑖 = 𝑖 𝑑𝑦𝑖 = 𝑗 𝑑
𝒅 × 𝒅
𝒙
𝒚
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N
𝑓 𝑖, 𝑗 : 1: N × 1: N → Λ = {𝑞𝑚𝑖𝑛: 𝑒: 𝑞𝑚𝑎𝑥}
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N
N
𝑓 𝑖, 𝑗 : 1: N × 1: N → Λ = {𝑞𝑚𝑖𝑛: 𝑒: 𝑞𝑚𝑎𝑥}
3 octets
1 octet
½ octet
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N
𝑓 𝑖, 𝑗 : 1: N × 1: N → Λ = {𝑞𝑚𝑖𝑛: 𝑒: 𝑞𝑚𝑎𝑥}
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N
𝑓 𝑖, 𝑗 : 1: N × 1: N → Λ = {𝑞𝑚𝑖𝑛: 𝑒: 𝑞𝑚𝑎𝑥}
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N
𝑓 𝑖, 𝑗 : 1: N × 1: N → Λ = {𝑞𝑚𝑖𝑛: 𝑒: 𝑞𝑚𝑎𝑥}
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N
𝑓 𝑖, 𝑗 : 1: N × 1: N → Λ = {𝑞𝑚𝑖𝑛: 𝑒: 𝑞𝑚𝑎𝑥}
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N
𝑓 𝑖, 𝑗 : 1: N × 1: N → Λ = {𝑞𝑚𝑖𝑛: 𝑒: 𝑞𝑚𝑎𝑥}
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N
N
𝑓 𝑖, 𝑗 : 1: N × 1: N → Λ = {𝑞𝑚𝑖𝑛: 𝑒: 𝑞𝑚𝑎𝑥}
𝑓 𝑖, 𝑗 = 𝑓 𝑥𝑖 = 𝑑𝑖, 𝑦𝑗 = 𝑑𝑗Λ
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𝑒𝑓 = 1
𝒇
𝒇N
N
𝑓 𝑖, 𝑗 : 1: N × 1: N → Λ = {𝑞𝑚𝑖𝑛: 𝑒: 𝑞𝑚𝑎𝑥}
𝑓 𝑖, 𝑗 = 𝑓 𝑥𝑖 = 𝑑𝑖, 𝑦𝑗 = 𝑑𝑗Λ
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N
𝑓 𝑖, 𝑗 = 𝛼 𝑓 𝑥𝑖 = 𝑑𝑖, 𝑦𝑗 = 𝑑𝑗 + 𝛽Λ
𝑒𝑓 = 0,2
𝒇
𝒇
𝑓 𝑖, 𝑗 : 1: N × 1: N → Λ = {𝑞𝑚𝑖𝑛: 𝑒: 𝑞𝑚𝑎𝑥}
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■N
N
𝑞𝑚𝑖𝑛
𝑞𝑚𝑎𝑥
𝑓 𝑖, 𝑗 : 1: N × 1: N → Λ = {𝑞𝑚𝑖𝑛: 𝑒: 𝑞𝑚𝑎𝑥}
𝑓 𝑖, 𝑗 = 𝛼 𝑓 𝑥𝑖 = 𝑑𝑖, 𝑦𝑗 = 𝑑𝑗 + 𝛽Λ
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𝑞𝑚𝑖𝑛
𝑞𝑚𝑎𝑥
N
N
𝑓 𝑖, 𝑗 : 1: N × 1: N → Λ = {𝑞𝑚𝑖𝑛: 𝑒: 𝑞𝑚𝑎𝑥}
𝑓 𝑖, 𝑗 = 𝛼 𝑓 𝑥𝑖 = 𝑑𝑖, 𝑦𝑗 = 𝑑𝑗 + 𝛽Λ
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𝑞𝑚𝑎𝑥
𝑞𝑚𝑖𝑛
𝒒𝒎𝒊𝒏 𝒒𝒎𝒂𝒙
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𝑓 𝑖, 𝑗 = 𝛼 𝑓 𝑥𝑖 = 𝑑𝑖, 𝑦𝑗 = 𝑑𝑗 + 𝛽Λ
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𝑞𝑚𝑎𝑥
𝑞𝑚𝑖𝑛
𝒒𝒎𝒊𝒏 𝒒𝒎𝒂𝒙
𝑓 𝑖, 𝑗 = 𝛼 𝑓 𝑥𝑖 = 𝑑𝑖, 𝑦𝑗 = 𝑑𝑗 + 𝛽Λ
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𝑞𝑚𝑎𝑥
𝑞𝑚𝑖𝑛
𝒒𝒎𝒊𝒏 𝒒𝒎𝒂𝒙
𝑓 𝑖, 𝑗 = 𝛼 𝑓 𝑥𝑖 = 𝑑𝑖, 𝑦𝑗 = 𝑑𝑗 + 𝛽Λ
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𝑞𝑚𝑎𝑥
𝑞𝑚𝑖𝑛
𝒒𝒎𝒊𝒏 𝒒𝒎𝒂𝒙
𝑓 𝑖, 𝑗 = 𝛼 𝑓 𝑥𝑖 = 𝑑𝑖, 𝑦𝑗 = 𝑑𝑗 + 𝛽Λ
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𝑓 𝑖, 𝑗 = 𝛼 𝑓 𝑥𝑖 = 𝑑𝑖, 𝑦𝑗 = 𝑑𝑗 + 𝛽Λ
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data set data set data set image44 49 43 4D128 bytes
𝑓 𝑖, 𝑗 = 𝛼 𝑓 𝑥𝑖 = 𝑑𝑖, 𝑦𝑗 = 𝑑𝑗 + 𝛽Λ
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group element
TAG
VR length value
data set data set data set image44 49 43 4D128 bytes
𝑓 𝑖, 𝑗 = 𝛼 𝑓 𝑥𝑖 = 𝑑𝑖, 𝑦𝑗 = 𝑑𝑗 + 𝛽Λ
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group element
TAG
VR length
data set data set data set image44 49 43 4D128 bytes
EXPLICIT
group element length IMPLICIT
value
valueVR
𝑓 𝑖, 𝑗 = 𝛼 𝑓 𝑥𝑖 = 𝑑𝑖, 𝑦𝑗 = 𝑑𝑗 + 𝛽Λ
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data set
group element VR length value
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data set
group element VR length value
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data set
group element VR length value
Date
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data set
group element VR length value
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data set
group element VR length value
Date : 12/03/2014
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data set
group element VR length value
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𝒅
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𝒙
𝒚
𝒙
𝒚
𝒇 𝒔 = 𝒇 ∗ 𝒉
𝒛
𝒉 (𝑳𝑴𝑯)
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𝒙
𝒚
𝒙
𝒚
𝒇 𝒔 = 𝒇 ∗ 𝒉
𝒉
𝒅 × 𝒅
𝒛
(𝑳𝑴𝑯)
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𝒙
𝒔
𝒉𝟐𝒉𝟏
𝒔 = 𝒉𝟏 + 𝒉𝟐
𝒅𝒊𝒔𝒕 < 𝑳𝑴𝑯
𝒙
𝒇
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𝒙
𝒔
𝒉𝟐𝒉𝟏
𝒔 = 𝒉𝟏 + 𝒉𝟐
𝒅𝒊𝒔𝒕 < 𝑳𝑴𝑯
𝒅
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𝒙
𝒔
𝒉𝟐𝒉𝟏
𝒔 = 𝒉𝟏 + 𝒉𝟐
𝒅𝒊𝒔𝒕 < 𝑳𝑴𝑯
𝒅𝒊𝒔𝒕 ≥ 𝑳𝑴𝑯
𝒅
𝒙
𝒔
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𝒙
𝒔
𝒉𝟐𝒉𝟏
𝒔 = 𝒉𝟏 + 𝒉𝟐
𝒅𝒊𝒔𝒕 < 𝑳𝑴𝑯
𝒅𝒊𝒔𝒕 ≥ 𝑳𝑴𝑯
𝒅
𝒅 ≤𝒅𝒊𝒔𝒕
𝟐
𝒙
𝒔
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𝒙
𝒔
𝒉𝟐𝒉𝟏
𝒔 = 𝒉𝟏 + 𝒉𝟐
𝒅𝒊𝒔𝒕 < 𝑳𝑴𝑯
𝒅𝒊𝒔𝒕 = 𝑳𝑴𝑯
𝒅
𝒅 =𝑳𝑴𝑯
𝟐
𝒙
𝒔
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𝒅𝒊𝒔𝒕 = 𝑳𝑴𝑯
𝒅 =𝑳𝑴𝑯
𝟐
𝒙
𝒔
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𝒅𝒊𝒔𝒕 = 𝑳𝑴𝑯
𝒅 =𝑳𝑴𝑯
𝟐
𝒙
𝒔
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𝒙
𝒔
𝝂
𝒔
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𝒙
𝒔
𝝂
𝒔
𝒙
𝒆 ×𝒅
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𝒙
𝒔
𝝂
𝒔
𝒙
𝒆
𝒅
𝒙
𝒔𝒆 = 𝒔 × 𝒆
×
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𝒙
𝒔
𝝂
𝒔
𝒙
𝒆
𝒙
𝒔𝒆 = 𝒔 × 𝒆
𝝂
𝒆× ∗𝟏/𝒅𝒅
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𝒙
𝒔
𝝂
𝒔
𝒙
𝒆
𝒙
𝒔𝒆 = 𝒔 × 𝒆
𝝂
𝒆× ∗
𝝂
𝒔𝒆 = 𝒔 ∗ 𝒆
𝒅 𝟏/𝒅
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𝒙
𝒔
𝝂
𝒔
𝒙
𝒆
𝒙
𝒔𝒆 = 𝒔 × 𝒆
𝝂
𝒆× ∗
𝝂
𝒔𝒆 = 𝒔 ∗ 𝒆
𝒔𝒆 𝒙 = 𝒔 𝒙
𝒏=−∞
+∞
𝜹(𝒙 − 𝒏𝒅)
𝒅 𝟏/𝒅
𝒔𝒆 𝒙 =
𝒏=−∞
+∞
𝒔(𝝂 − 𝒏 𝝂𝒆)
𝝂𝒆 = 𝟏/𝒅
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𝝂
= 𝒔 ∗ 𝒆 =
𝒏=−∞
+∞
𝒔(𝝂 − 𝒏 𝝂𝒆)
𝟐 𝝂𝒆−𝟐 𝝂𝒆 −𝝂𝒆 𝟎
𝒔𝒆
𝝂𝒆
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𝝂
𝝂𝒆 𝟐 𝝂𝒆−𝟐 𝝂𝒆 −𝝂𝒆 𝟎 𝝂𝒎𝒂𝒙
𝝂 > 𝝂𝒎𝒂𝒙 ∶ 𝒔 𝝂 = 0
= 𝒔 ∗ 𝒆 =
𝒏=−∞
+∞
𝒔(𝝂 − 𝒏 𝝂𝒆) 𝒔𝒆
−𝝂𝒎𝒂𝒙
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𝝂
𝝂𝒆 𝟐 𝝂𝒆−𝟐 𝝂𝒆 −𝝂𝒆 𝟎 𝝂𝒎𝒂𝒙
𝝂
𝒘𝟏×
= 𝒔 ∗ 𝒆 =
𝒏=−∞
+∞
𝒔(𝝂 − 𝒏 𝝂𝒆) 𝒔𝒆
−𝝂𝒎𝒂𝒙
𝝂𝒆/𝟐−𝝂𝒆/𝟐
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𝝂
𝝂𝒆 𝟐 𝝂𝒆−𝟐 𝝂𝒆 −𝝂𝒆 𝟎 𝝂𝒎𝒂𝒙
𝝂
𝒘𝟏
= 𝒔 ∗ 𝒆 =
𝒏=−∞
+∞
𝒔(𝝂 − 𝒏 𝝂𝒆) 𝒔𝒆
? 𝒔𝒆 × 𝒘 = 𝒔
−𝝂𝒎𝒂𝒙
×
𝝂𝒆/𝟐−𝝂𝒆/𝟐
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𝝂
𝝂𝒆 𝟐 𝝂𝒆−𝟐 𝝂𝒆 −𝝂𝒆 𝟎 𝝂𝒎𝒂𝒙
𝝂
𝒘𝟏
= 𝒔 ∗ 𝒆 =
𝒏=−∞
+∞
𝒔(𝝂 − 𝒏 𝝂𝒆) 𝒔𝒆
𝝂𝒆 − 𝝂𝒎𝒂𝒙
? 𝒔𝒆 × 𝒘 = 𝒔
−𝝂𝒎𝒂𝒙
×
𝝂𝒆/𝟐−𝝂𝒆/𝟐
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𝝂
𝝂𝒆 𝟐 𝝂𝒆−𝟐 𝝂𝒆 −𝝂𝒆 𝟎 𝝂𝒎𝒂𝒙
𝝂
𝒘𝟏
= 𝒔 ∗ 𝒆 =
𝒏=−∞
+∞
𝒔(𝝂 − 𝒏 𝝂𝒆) 𝒔𝒆
?
𝝂𝒆 − 𝝂𝒎𝒂𝒙
𝝂𝒎𝒂𝒙 ≤ 𝝂𝒆/𝟐𝝂𝒆 − 𝝂𝒎𝒂𝒙 ≥ 𝝂𝒆/𝟐
𝒔𝒆 × 𝒘 = 𝒔
−𝝂𝒎𝒂𝒙
×
𝝂𝒆/𝟐−𝝂𝒆/𝟐
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𝝂
𝝂𝒆 𝟐 𝝂𝒆−𝟐 𝝂𝒆 −𝝂𝒆 𝟎 𝝂𝒎𝒂𝒙
𝝂
𝒘𝟏
𝒔𝒆 × 𝒘 = 𝒔𝒔𝒔𝒊
𝝂𝒆 ≥ 𝟐 𝝂𝒎𝒂𝒙
= 𝒔 ∗ 𝒆 =
𝒏=−∞
+∞
𝒔(𝝂 − 𝒏 𝝂𝒆) 𝒔𝒆
𝝂𝒆 − 𝝂𝒎𝒂𝒙
−𝝂𝒎𝒂𝒙
×
𝝂𝒆/𝟐−𝝂𝒆/𝟐
𝝂𝒎𝒂𝒙 ≤ 𝝂𝒆/𝟐𝝂𝒆 − 𝝂𝒎𝒂𝒙 ≥ 𝝂𝒆/𝟐
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𝝂
𝝂𝒆 𝟐 𝝂𝒆−𝟐 𝝂𝒆 −𝝂𝒆 𝟎 𝝂𝒎𝒂𝒙
𝝂
𝒘𝟏
𝒔𝒆 × 𝒘 = 𝒔 ⇔ 𝒔 = 𝒔𝒆 ∗ 𝒘𝒔𝒔𝒊
𝝂𝒆 ≥ 𝟐 𝝂𝒎𝒂𝒙
= 𝒔 ∗ 𝒆 =
𝒏=−∞
+∞
𝒔(𝝂 − 𝒏 𝝂𝒆) 𝒔𝒆
𝝂𝒆 − 𝝂𝒎𝒂𝒙
−𝝂𝒎𝒂𝒙
×
𝝂𝒆/𝟐−𝝂𝒆/𝟐
𝝂𝒎𝒂𝒙 ≤ 𝝂𝒆/𝟐𝝂𝒆 − 𝝂𝒎𝒂𝒙 ≥ 𝝂𝒆/𝟐
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𝝂
𝝂𝒆 𝟐 𝝂𝒆−𝟐 𝝂𝒆 −𝝂𝒆 𝟎 𝝂𝒎𝒂𝒙−𝝂𝒎𝒂𝒙
𝝂
𝒘𝟏
𝒔𝒆 × 𝒘 = 𝒔 ⇔ 𝒔 = 𝒔𝒆 ∗ 𝒔𝒊𝒏𝒄(𝒙/𝒅)𝒔𝒔𝒊
𝝂𝒆 ≥ 𝟐 𝝂𝒎𝒂𝒙
= 𝒔 ∗ 𝒆 =
𝒏=−∞
+∞
𝒔(𝝂 − 𝒏 𝝂𝒆) 𝒔𝒆
𝝂𝒆 − 𝝂𝒎𝒂𝒙
𝒔𝒊𝒏𝒄(𝒙)
×
𝝂𝒆/𝟐−𝝂𝒆/𝟐
𝝂𝒎𝒂𝒙 ≤ 𝝂𝒆/𝟐𝝂𝒆 − 𝝂𝒎𝒂𝒙 ≥ 𝝂𝒆/𝟐
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𝒙
𝒔
𝒙
𝒔𝒆
𝒔𝒆 𝒙 = 𝒔 𝒙
𝒏=−∞
+∞
𝜹(𝒙 − 𝒏𝒅)× 𝒆
𝝂𝒆 ≥ 𝟐 𝝂𝒎𝒂𝒙 ∶ 𝒅 ≤𝟏
𝟐 𝝂𝒎𝒂𝒙
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𝒙
𝒔
𝒙
𝒔𝒆
𝒔𝒆 𝒙 = 𝒔 𝒙
𝒏=−∞
+∞
𝜹(𝒙 − 𝒏𝒅)
𝒙
𝒔𝒔 𝒙 = 𝒔𝒆 𝒙 ∗ 𝒔𝒊𝒏𝒄(𝒙/𝒅)
∗ 𝒔𝒊𝒏𝒄
× 𝒆
𝝂𝒆 ≥ 𝟐 𝝂𝒎𝒂𝒙 ∶ 𝒅 ≤𝟏
𝟐 𝝂𝒎𝒂𝒙
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𝝂
𝝂𝒆 𝟐 𝝂𝒆−𝟐 𝝂𝒆 −𝝂𝒆 𝟎 𝝂𝒎𝒂𝒙−𝝂𝒎𝒂𝒙
= 𝒔 ∗ 𝒆 =
𝒏=−∞
+∞
𝒔(𝝂 − 𝒏 𝝂𝒆) 𝒔𝒆𝝂𝒆 < 𝟐 𝝂𝒎𝒂𝒙
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𝝂
𝝂𝒆 𝟐 𝝂𝒆−𝟐 𝝂𝒆 −𝝂𝒆 𝟎
= 𝒔 ∗ 𝒆 =
𝒏=−∞
+∞
𝒔(𝝂 − 𝒏 𝝂𝒆) 𝒔𝒆𝝂𝒆 < 𝟐 𝝂𝒎𝒂𝒙
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𝝂
𝝂𝒆 𝟐 𝝂𝒆−𝟐 𝝂𝒆 −𝝂𝒆
= 𝒔 ∗ 𝒆 =
𝒏=−∞
+∞
𝒔(𝝂 − 𝒏 𝝂𝒆) 𝒔𝒆𝝂𝒆 < 𝟐 𝝂𝒎𝒂𝒙
𝝂
𝟎
𝟎 𝝂𝒎𝒂𝒙−𝝂𝒎𝒂𝒙
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𝝂
𝝂𝒆 𝟐 𝝂𝒆−𝟐 𝝂𝒆 −𝝂𝒆
= 𝒔 ∗ 𝒆 =
𝒏=−∞
+∞
𝒔(𝝂 − 𝒏 𝝂𝒆) 𝒔𝒆𝝂𝒆 < 𝟐 𝝂𝒎𝒂𝒙
𝝂
𝟎
𝟎 𝝂𝒆−𝝂𝒆
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𝝂
𝝂𝒆 𝟐 𝝂𝒆−𝟐 𝝂𝒆 −𝝂𝒆
= 𝒔 ∗ 𝒆 =
𝒏=−∞
+∞
𝒔(𝝂 − 𝒏 𝝂𝒆) 𝒔𝒆𝝂𝒆 < 𝟐 𝝂𝒎𝒂𝒙
𝝂
𝟎
𝟎 𝝂𝒆−𝝂𝒆 𝝂𝒆/2−𝝂𝒆/2
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𝝂
𝝂𝒆 𝟐 𝝂𝒆−𝟐 𝝂𝒆 −𝝂𝒆 𝟎
= 𝒔 ∗ 𝒆 =
𝒏=−∞
+∞
𝒔(𝝂 − 𝒏 𝝂𝒆) 𝒔𝒆𝝂𝒆 < 𝟐 𝝂𝒎𝒂𝒙
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𝝂
𝝂𝒆 𝟐 𝝂𝒆−𝟐 𝝂𝒆 −𝝂𝒆 𝟎
= 𝒔 ∗ 𝒆 =
𝒏=−∞
+∞
𝒔(𝝂 − 𝒏 𝝂𝒆) 𝒔𝒆𝝂𝒆 < 𝟐 𝝂𝒎𝒂𝒙
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𝝂
𝝂𝒆 𝟐 𝝂𝒆−𝟐 𝝂𝒆 −𝝂𝒆 𝟎
= 𝒔 ∗ 𝒆 =
𝒏=−∞
+∞
𝒔(𝝂 − 𝒏 𝝂𝒆) 𝒔𝒆𝝂𝒆 < 𝟐 𝝂𝒎𝒂𝒙
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𝝂
𝝂𝒆 𝟐 𝝂𝒆−𝟐 𝝂𝒆 −𝝂𝒆 𝟎
= 𝒔 ∗ 𝒆 =
𝒏=−∞
+∞
𝒔(𝝂 − 𝒏 𝝂𝒆) 𝒔𝒆𝝂𝒆 < 𝟐 𝝂𝒎𝒂𝒙
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𝒔 𝒙 = 𝒔𝒆 𝒙 ∗ 𝒔𝒊𝒏𝒄(𝝂𝒆𝒙)
𝝂𝒆 = 𝟎, 𝟖 𝝂𝒎𝒂𝒙 𝝂𝒆 = 𝟏, 𝟐𝟓 𝝂𝒎𝒂𝒙
𝝂𝒆 = 𝟐 𝝂𝒎𝒂𝒙 𝝂𝒆 = 𝟓 𝝂𝒎𝒂𝒙
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𝒙
𝒚
𝒙
𝒚
𝒇
𝒔 = 𝒇 ∗ 𝒉
𝒛
𝒉 (𝑳𝑴𝑯)
𝑳𝑴𝑯 𝑳𝑴𝑯 𝒔 = 𝒇 𝒉
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𝒙
𝒚
𝒙
𝒚
𝒇
𝒛
𝒉 (𝑳𝑴𝑯)
𝑳𝑴𝑯 𝑳𝑴𝑯
𝝂𝒎𝒂𝒙 ≈𝟏
𝑳𝑴𝑯
𝝂
𝟏/𝑳𝑴𝑯
𝒉(𝝂)
𝒔 = 𝒇 ∗ 𝒉
𝒔 = 𝒇 𝒉
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𝒙
𝒚
𝒙
𝒚
𝒇
𝒛
𝒉 (𝑳𝑴𝑯)
𝑳𝑴𝑯
𝝂𝒎𝒂𝒙 ≈𝟏
𝑳𝑴𝑯 𝒉(𝝂)
𝝂𝒆 =𝟐
𝑳𝑴𝑯; 𝒅 =
𝑳𝑴𝑯
𝟐
𝒅 × 𝒅
𝒔 = 𝒇 ∗ 𝒉
𝒔 = 𝒇 𝒉
𝝂
𝟏/𝑳𝑴𝑯
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𝒙
𝒚
𝒛
𝑳𝑴𝑯 𝒉
𝟓 → 𝟏𝟓𝒎𝒎
𝐍 = 𝟐𝟓𝟔 ∶ 𝒅 =𝟓𝟎𝟎
𝟐𝟓𝟔≈ 𝟐𝒎𝒎 ≪
𝑳𝑴𝑯
𝟐
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𝒙
𝒚
𝒛
𝑳𝑴𝑯 𝒉
𝟓 → 𝟏𝟓𝒎𝒎
𝐍 = 𝟏𝟐𝟖 ∶ 𝒅 =𝟓𝟎𝟎
𝟏𝟐𝟖≈ 𝟒𝒎𝒎 ≈
𝑳𝑴𝑯
𝟐
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𝒙
𝒚
𝒛
𝒅 ≈ 𝟐 − 𝟑𝒎𝒎
Taille du détecteur
Démultiplexage
Non collinéarité
Portée moyenne
Astigmatisme radial
𝑳𝑴𝑯 𝒉
𝟒 → 𝟏𝟎𝒎𝒎
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= +
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= +
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𝝋 = 𝒇 ∗ 𝒉
𝝋 = 𝒇 𝒉
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𝝋 = 𝒇 ∗ 𝒉
𝝋 = 𝒇 𝒉
𝒉
𝝋𝒊,𝒋 =
𝒎=−𝟏
𝟏
𝒏=−𝟏
𝟏
𝒇𝒊−𝒎,𝒋−𝒏 𝒉𝒎,𝒏
𝒉 =1
4
0,25 0,5 0,250,5 1 0,50,25 0,5 0,25
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𝝋 = 𝒇 ∗ 𝒉
𝝋 = 𝒇 𝒉
𝒉
𝝋 𝜈𝑖 , 𝜈𝑗 = 𝒇 𝜈𝑖 , 𝜈𝑗 𝒉 𝜈𝑖 , 𝜈𝑗
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𝒉 𝜈 =1
1 +𝜈𝜈𝐶
2𝑛
𝟏/ 𝟐
𝝂𝑪
𝝂
𝒉 𝝂 𝒏
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𝒉 𝜈𝑖 , 𝜈𝑗 =1
1 +𝜈𝑖2 + 𝜈𝑗
2
𝜈𝐶
2𝑛
𝜈𝐶 = 60%𝑛 = 4
𝜈𝐶 = 60%𝑛 = 12
𝜈𝐶 = 30%𝑛 = 4
𝜈𝐶 = 30%𝑛 = 12
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𝒉 𝜈𝑖 , 𝜈𝑗 =1
1 +𝜈𝑖2 + 𝜈𝑗
2
𝜈𝐶
2𝑛
𝜈𝐶 = 50%𝑛 = 20
𝜈𝐶 = 25%𝑛 = 20
𝜈𝐶 = 25%𝑛 = 2
𝜈𝐶 = 50%𝑛 = 2
𝜈𝐶 = 75%𝑛 = 20
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𝛁𝑓(𝑥) = lim𝜀→0
𝑓 𝑥 + 𝜀 − 𝑓(𝑥 − 𝜀)
2𝜀𝑚𝑎𝑥(𝛁𝑓)
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𝑚𝑎𝑥(𝛁𝑓)𝛁𝑓(𝑥) = lim
𝜀→0
𝑓 𝑥 + 𝜀 − 𝑓(𝑥 − 𝜀)
2𝜀
𝒉 = 𝛁𝒙 =−0,5 0 0,5−1 0 1−0,5 0 0,5
𝒉 = 𝛁𝒚 =−0,5 −1 −0,50 0 00,5 1 0,5
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𝒉 = 𝛁𝒙 =−0,5 0 0,5−1 0 1−0,5 0 0,5
𝒉 = 𝛁𝒚 =−0,5 −1 −0,50 0 00,5 1 0,5
𝒉 = 𝛁𝒙2 + 𝛁𝒚
2
𝑚𝑎𝑥(𝛁𝑓)𝛁𝑓(𝑥) = lim
𝜀→0
𝑓 𝑥 + 𝜀 − 𝑓(𝑥 − 𝜀)
2𝜀
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𝚫𝑓(𝑥) = lim𝜀→0
𝑓 𝑥 + 𝜀 − 2𝑓 𝑥 + 𝑓(𝑥 − 𝜀)
𝜀²𝚫𝑓 = 0
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𝒉 =0 −0,25 0
−0,25 1 −0,250 −0,25 0
𝒉 =−0,125 −0,125 −0,125−0,125 1 −0,125−0,125 −0,125 −0,125
𝒉 =0,25 −0,5 0,25−0,5 1 −0,50,25 −0,5 0,25
𝚫𝑓 = 0 𝚫𝑓(𝑥) = lim𝜀→0
𝑓 𝑥 + 𝜀 − 2𝑓 𝑥 + 𝑓(𝑥 − 𝜀)
𝜀²
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𝒙
𝒚
𝒙
𝒚
𝒇
𝒛
𝒉
𝝋 = 𝒇 ∗ 𝒉
𝝋 = 𝒇 𝒉
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𝒙
𝒚
𝒙
𝒚
𝒇
𝒛
𝒉
𝝋 = 𝒇 ∗ 𝒉
𝒇 = 𝝋
𝒉𝒇 = 𝝋 ∗
𝟏
𝒉
𝝋 = 𝒇 𝒉
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𝒉𝒉
𝑥
𝐿𝑀𝐻
𝜈
𝜈𝑚𝑎𝑥
𝝋 = 𝒇 ∗ 𝒉 𝝋 = 𝒇 𝒉
𝑳𝑴𝑯
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𝟏
𝒉
𝟏
𝒉
𝒇 = 𝝋
𝒉
𝒇 = 𝝋 ∗ 𝟏/ 𝒉𝑥
𝐿𝑀𝐻
𝒉𝒉
𝑥
𝐿𝑀𝐻
𝜈
𝜈𝑚𝑎𝑥
𝝋 = 𝒇 ∗ 𝒉 𝝋 = 𝒇 𝒉
𝑳𝑴𝑯
𝜈
𝜈𝑚𝑎𝑥
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𝒇 = 𝝋 𝒎𝒏
𝒎𝒏 =1 − 1 − 𝒉2 𝑛
𝒉
𝒇 = 𝝋
𝒉
𝜈
𝜈𝑚𝑎𝑥
𝒎
1
𝒉
𝒏 = 𝟏
𝟐𝟒
𝟖
𝟏𝟔
𝟓𝟎
𝟏𝟎𝟎
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𝒇 = 𝝋 𝒎𝒏
𝒇 = 𝝋
𝒉
𝜈
𝜈𝑚𝑎𝑥
1
𝒉
𝒏 = 𝟏
𝟐𝟒
𝟖
𝟏𝟔
𝟓𝟎
𝟏𝟎𝟎
𝒏 = 𝟏
𝟒
𝟏𝟔
𝟏𝟎𝟎
𝒎𝒏 𝒎𝒏
𝒇 = 𝝋 ∗ 𝒎𝒏
𝒎𝒏 =1 − 1 − 𝒉2 𝑛
𝒉
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𝒇 = 𝝋
𝒉
𝜈
𝜈𝑚𝑎𝑥
1
𝒉
𝒏 = 𝟏
𝟐𝟒
𝟖
𝟏𝟔
𝟓𝟎
𝟏𝟎𝟎
𝒏 = 𝟏
𝟒
𝟏𝟔
𝟏𝟎𝟎
𝒇 = 𝝋 𝒎𝒏
𝒎𝒏 𝒎𝒏
𝒇 = 𝝋 ∗ 𝒎𝒏
𝑛 = 0,834 ln 𝐶 − 7,774
King et al. J Nucl Med 1988
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𝑥
𝑦
s
θ
s
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𝑥
𝑦
s
θ
s
𝑥
𝑦
s
θϕ
R
s
D
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𝑥
𝑦
s
θ
s
𝑥
𝑦
s
θϕ
D
s
ϕ
R
R
s θ = R cos θ − ϕ
s′ θ = R sin ϕ − θ = D
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𝑥
𝑦
s
θ
s
𝑥
𝑦
s
θϕ
D
s
R
ΔsΔθ
𝚫𝐬
𝚫𝛉= 𝐃
s θ = R cos θ − ϕ
s′ θ = R sin ϕ − θ = D
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𝑥
𝑦
s
θ
s
𝑥
𝑦
D
s
𝚫𝐬
𝚫𝛉= 𝐃
s θ = R cos θ − ϕ
s′ θ = R sin ϕ − θ = D
D
D
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𝑥
𝑦
s
θ
s
𝑥
𝑦
D
s
𝚫𝐬
𝚫𝛉= 𝐃
s θ = R cos θ − ϕ
s′ θ = R sin ϕ − θ = D
ω
k
TF
𝐤
𝛚= −𝐃
D
D
𝐤
𝛚
![Page 110: TRAITEMENT des IMAGES MEDICALES · group element TAG VR length 128 bytes 44 49 43 4D data set data set data set image EXPLICIT group element length IMPLICIT value VR value , = = ,](https://reader034.vdocuments.net/reader034/viewer/2022050412/5f8967faf33fec53bf0c71ac/html5/thumbnails/110.jpg)
𝑥
𝑦
s
θ
s
s ω
k
TF
𝐝𝐢𝐬𝐭 = 𝐁 + 𝐃
= 𝐁 −𝐤
𝛚𝑥
𝑦
s
θ
D
B
𝐤
𝛚
![Page 111: TRAITEMENT des IMAGES MEDICALES · group element TAG VR length 128 bytes 44 49 43 4D data set data set data set image EXPLICIT group element length IMPLICIT value VR value , = = ,](https://reader034.vdocuments.net/reader034/viewer/2022050412/5f8967faf33fec53bf0c71ac/html5/thumbnails/111.jpg)
𝑥
𝑦
s
θ
s
s ω
k
TF
𝐝𝐢𝐬𝐭 = 𝐁 + 𝐃
= 𝐁 −𝐤
𝛚𝑥
𝑦
s
θ
D
B
𝐤
𝛚
𝒇 = 𝝋 𝒎
𝑳𝑴𝑯