Introducton to Medical Iaaee rrocessine
Iaaee Fundaaentals and Spatal Filterine:
Image is key in diagnosis and treatment of many diseases (e.g. oncology), they have to be
interpreted and analyzed. In automatc processing you have to keep in mind possible false
alarms.
Framework for image analysis:
Sampling: digitzing the coordinate values.
Quantzaton: digitzing the amplitude (intensity) values.
Spatal domain techniques can be denoted by the eppression: g(p,y)T[ff(p,y)C.
F(p,y): input image
G(p,y) output or processed image.
[: operater defned on a neighborhood around (p,y).
Image blurring eliminates small details, renders largest regions of the image (‘blobs’ ) and
removes noise.
Probability of occurrence of intensity level rk T pr(rk)Tnk/MN, k T0,1,2 …,L-1
MN: total number of pipels in the image.
Nk: number of pipels that have intensity rk
L: number of possible intensity levels in the image.
A plot of pr(rk) is a histogram.
Histogram equalizaton is a cumulatve distributon functon of random variable rk.
k
SkT[(rk)T(L-1)∑ p r (r j), where k T 0,1,2, …, L-1.
j=0
Epample for histogram equalizaton. You have the
intensity distributon of fgure 1. Number of intensity
levels is L, which is 8. MN is total number of pipels. N k is
the number of pipels with this intensity. rk is the
intensity level and pr(rk) is the probability of a pipel
having intensity level rk . [he frst graph is the original
histogram, than you see the transformaton functon
Figuur 1
1
, and lastly the equalized histogram. [he values for the transformaton functon are caluclated
by Sk T (L-1)*pr(rk). so this gives s0 for instance 7*0,19T1.33≈1.
It is an efcient tool for increasing contrast, for a wide variety of images. However, the
algorithm is not discriminatve to noise, it doesn’t take into account spatal correlaton
between pipels and it can produce unrealistc efects in images due to color changes.
Linear spatal fltering: multply each pipel in the neighborhood by a corresponding
coefcient and sum the results to obtain the response at each point.
Nonlinear spatal fltering performs nonlinear operatons on neighborhood pipels. Median
fltering consists of replacing each pipel by the median of its neighborhood. With an adaptve
median flter you compute the mapimum, minimum and medium of the neighborhood. [hen
you check if min < med < map.
Average flter:
In a 3by3 neighborhood, the new value for the 7 will be:
(5+1+3+0+7+1+1+2+3)/9≈3. When it is on the edges you can use 0 for
every unknown value, but this is unlikely to be true. You can also mirror
the values on the edge.
2
Iaaee Fundaaentals and Spatal Filterine:
Image is key in diagnosis and treatment of many diseases (e.g. oncology), they have to be
interpreted and analyzed. In automatc processing you have to keep in mind possible false
alarms.
Framework for image analysis:
Sampling: digitzing the coordinate values.
Quantzaton: digitzing the amplitude (intensity) values.
Spatal domain techniques can be denoted by the eppression: g(p,y)T[ff(p,y)C.
F(p,y): input image
G(p,y) output or processed image.
[: operater defned on a neighborhood around (p,y).
Image blurring eliminates small details, renders largest regions of the image (‘blobs’ ) and
removes noise.
Probability of occurrence of intensity level rk T pr(rk)Tnk/MN, k T0,1,2 …,L-1
MN: total number of pipels in the image.
Nk: number of pipels that have intensity rk
L: number of possible intensity levels in the image.
A plot of pr(rk) is a histogram.
Histogram equalizaton is a cumulatve distributon functon of random variable rk.
k
SkT[(rk)T(L-1)∑ p r (r j), where k T 0,1,2, …, L-1.
j=0
Epample for histogram equalizaton. You have the
intensity distributon of fgure 1. Number of intensity
levels is L, which is 8. MN is total number of pipels. N k is
the number of pipels with this intensity. rk is the
intensity level and pr(rk) is the probability of a pipel
having intensity level rk . [he frst graph is the original
histogram, than you see the transformaton functon
Figuur 1
1
, and lastly the equalized histogram. [he values for the transformaton functon are caluclated
by Sk T (L-1)*pr(rk). so this gives s0 for instance 7*0,19T1.33≈1.
It is an efcient tool for increasing contrast, for a wide variety of images. However, the
algorithm is not discriminatve to noise, it doesn’t take into account spatal correlaton
between pipels and it can produce unrealistc efects in images due to color changes.
Linear spatal fltering: multply each pipel in the neighborhood by a corresponding
coefcient and sum the results to obtain the response at each point.
Nonlinear spatal fltering performs nonlinear operatons on neighborhood pipels. Median
fltering consists of replacing each pipel by the median of its neighborhood. With an adaptve
median flter you compute the mapimum, minimum and medium of the neighborhood. [hen
you check if min < med < map.
Average flter:
In a 3by3 neighborhood, the new value for the 7 will be:
(5+1+3+0+7+1+1+2+3)/9≈3. When it is on the edges you can use 0 for
every unknown value, but this is unlikely to be true. You can also mirror
the values on the edge.
2
