Seminar hasil penelitian ekstraksi fitur bentuk dan venasi citra daun dengan pemodelan fourier dan b-spline
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 SEMINAR HASIL PENELITIAN EKSTRAKSI FITUR BENTUK DAN VENASI CITRA DAUN DENGAN PEMODELAN FOURIER DAN B-SPLINERahmadhani M Yeni Herdiyeni, S.Si., M.Kom. Latar Belakang Latar Belakang
 Contoh Karakter Daun Penelitian Terkait Tujuan Ruang LingkupFokus:  Metodologi Penelitian Data Penelitian
 Data Penelitian (2) Ekstraksi Fitur Bentuk Pengukuran Tingkat Kemiripan Ekstraksi Venasi Pencarian Struktur Evaluasi
Menggunakan sistem:
Evaluasi visual:  Evaluasi Hasil Temu Kembali  Hasil Ekstraksi Bentuk Hasil Ekstraksi Bentuk Recall-Precision Hasil Ekstraksi Venasi Tabulasi Total Nilai Kesesuaian Why too low accuracy? Kesimpulan
Plus: automasi inisialisasi parameter pencarian awal Hasil ekstraksi venasi citra daun secara umum kurang sesuai better capture of photos ekstraksi bentuk dengan pendekatan kurva yang lain seperti pemodelanBezierekstraksi venasi pada citra daun yang lebih baikPenelitian ukuran kesamaan antara satu set b-spline dengan satu set b-spline lainnya |
Tinjauan Pustaka
Fourier Descriptors
Fourier descriptors describe the shape in terms of its spatial frequency content.
Begin by representing the boundary of the shape as a periodic function (in one of a few possible ways).
Expand this in a Fourier series; obtain a set of coefficients that capture shape information.
Fourier Descriptors (cont.)
imagining that the image plane is complex
Fourier Descriptors (cont.)
• The truncated series is
The period is made equal to 2π by choosing the speed at which we circumnavigate the shape properly
Fourier Descriptors (cont.)
The k-th Fourier transform coefficient is calculated as
Shape feature must be invariant to rotation, translation, and dilatation effect. For satisfying these, some adjustments on Fourier descriptors should be done
Fourier Descriptors (cont.)
B-Spline
Polynomial curves
Ck-1 continuity
Cubic B-spline:
C2 continuity
B-Spline (cont.)
Knots • A sequence of scalar values t1, …, t2k with ti≠tj if i≠j, and ti< tj for i
• If ti chosen at uniform interval (such as 1,2,3, …), than it is a uniform knot sequence
B-Spline (cont.)
Control points We can define a unique k degree polynomial F(t) with blossom f, such that
Vi = f(ti+1,ti+2, …,ti+k) The sequence of vi for i [0,k] are the control points of a B-spline
Evaluation of a point on a curve with f(t,t,t)
Remark: no control points will lie on the curve!
B-Spline (cont.)
Given a sequence of knots, t1,…t2k,
For each interval [ti, ti+1], there’s a kth degree parametric curve F(t) defined with corresponding B-spline control points vi-k,vi-k+1, … , vi
If f() is the k-parameter blossom associated to the curve, then
B-Spline (cont.)
The control point are defined by vi =f(tj+1, …, tj+k), j=i-k, i-k, …, I
The k-th degree Bézier curve corresponding to this curve has the control points:
pj =f(ti, ti, …, ti,ti+1,ti+1,…, ti+1), where j = 0, 1, …, k The evaluation of the point on the curve at
t ∈[ti ,ti+1] is given by F(t) = f(t,t,…,t)
B-Splines Blending Functions
B-Splines Blending Functions Cox-deBoors Recurrence
Standard hough transform
Line equation: y=mx+c presenting in parameter space (c,m)
But this is wrong for vertical lines.
So polar co-ordinates are used as parameter space, i.e. (r,Θ) instead of (c,m).
Standard hough transform (cont.)
Standard hough transform (cont.)
Advantages of Parameterization
- Values of ‘r’ and ‘q’ become bounded
How to find intersection of the parametric curves
- Use of accumulator arrays
- concept of ‘Voting’
- To reduce the computational load use Gradient information
SHT Algorithm
Quantize the Hough Transform space: identify the maximum and minimum values of r and q
Generate an accumulator array A(r, q); set all values to zero
For all edge points (xi, yi) in the image
- Use gradient direction for q
- Compute r from the equation
- Increment A(r, q) by one
For all cells in A(r, q)
- Search for the maximum value of A(r, q)
- Calculate the equation of the line
To reduce the effect of noise more than one element (elements in a neighborhood) in the accumulator array are increased
SHT Algorithm(cont.)
• A sequence of scalar values t1, …, t2k with ti≠tj if i≠j, and ti< tj for i
• If ti chosen at uniform interval (such as 1,2,3, …), than it is a uniform knot sequence
B-Spline (cont.)
Control points We can define a unique k degree polynomial F(t) with blossom f, such that
Vi = f(ti+1,ti+2, …,ti+k) The sequence of vi for i [0,k] are the control points of a B-spline
Evaluation of a point on a curve with f(t,t,t)
Remark: no control points will lie on the curve!
B-Spline (cont.)
Given a sequence of knots, t1,…t2k,
For each interval [ti, ti+1], there’s a kth degree parametric curve F(t) defined with corresponding B-spline control points vi-k,vi-k+1, … , vi
If f() is the k-parameter blossom associated to the curve, then
B-Spline (cont.)
The control point are defined by vi =f(tj+1, …, tj+k), j=i-k, i-k, …, I
The k-th degree Bézier curve corresponding to this curve has the control points:
pj =f(ti, ti, …, ti,ti+1,ti+1,…, ti+1), where j = 0, 1, …, k The evaluation of the point on the curve at
t ∈[ti ,ti+1] is given by F(t) = f(t,t,…,t)
B-Splines Blending Functions
B-Splines Blending Functions Cox-deBoors Recurrence
Standard hough transform
Line equation: y=mx+c presenting in parameter space (c,m)
But this is wrong for vertical lines.
So polar co-ordinates are used as parameter space, i.e. (r,Θ) instead of (c,m).
Standard hough transform (cont.)
Standard hough transform (cont.)
Advantages of Parameterization
- Values of ‘r’ and ‘q’ become bounded
How to find intersection of the parametric curves
- Use of accumulator arrays
- concept of ‘Voting’
- To reduce the computational load use Gradient information
SHT Algorithm
Quantize the Hough Transform space: identify the maximum and minimum values of r and q
Generate an accumulator array A(r, q); set all values to zero
For all edge points (xi, yi) in the image
- Use gradient direction for q
- Compute r from the equation
- Increment A(r, q) by one
For all cells in A(r, q)
- Search for the maximum value of A(r, q)
- Calculate the equation of the line
To reduce the effect of noise more than one element (elements in a neighborhood) in the accumulator array are increased
SHT Algorithm(cont.)
We can define a unique k degree polynomial F(t) with blossom f, such that
The sequence of vi for i [0,k] are the control points of a B-spline
Evaluation of a point on a curve with f(t,t,t)
Remark: no control points will lie on the curve!
B-Spline (cont.)
Given a sequence of knots, t1,…t2k,
For each interval [ti, ti+1], there’s a kth degree parametric curve F(t) defined with corresponding B-spline control points vi-k,vi-k+1, … , vi
If f() is the k-parameter blossom associated to the curve, then
B-Spline (cont.)
The control point are defined by vi =f(tj+1, …, tj+k), j=i-k, i-k, …, I
The k-th degree Bézier curve corresponding to this curve has the control points:
pj =f(ti, ti, …, ti,ti+1,ti+1,…, ti+1), where j = 0, 1, …, k The evaluation of the point on the curve at
t ∈[ti ,ti+1] is given by F(t) = f(t,t,…,t)
B-Splines Blending Functions
B-Splines Blending Functions Cox-deBoors Recurrence
Standard hough transform
Line equation: y=mx+c presenting in parameter space (c,m)
But this is wrong for vertical lines.
So polar co-ordinates are used as parameter space, i.e. (r,Θ) instead of (c,m).
Standard hough transform (cont.)
Standard hough transform (cont.)
Advantages of Parameterization
- Values of ‘r’ and ‘q’ become bounded
How to find intersection of the parametric curves
- Use of accumulator arrays
- concept of ‘Voting’
- To reduce the computational load use Gradient information
SHT Algorithm
Quantize the Hough Transform space: identify the maximum and minimum values of r and q
Generate an accumulator array A(r, q); set all values to zero
For all edge points (xi, yi) in the image
- Use gradient direction for q
- Compute r from the equation
- Increment A(r, q) by one
For all cells in A(r, q)
- Search for the maximum value of A(r, q)
- Calculate the equation of the line
To reduce the effect of noise more than one element (elements in a neighborhood) in the accumulator array are increased
SHT Algorithm(cont.)
The evaluation of the point on the curve at
t ∈[ti ,ti+1] is given by F(t) = f(t,t,…,t)
B-Splines Blending Functions
B-Splines Blending Functions Cox-deBoors Recurrence
Standard hough transform
Line equation: y=mx+c presenting in parameter space (c,m)
But this is wrong for vertical lines.
So polar co-ordinates are used as parameter space, i.e. (r,Θ) instead of (c,m).
Standard hough transform (cont.)
Standard hough transform (cont.)
Advantages of Parameterization
- Values of ‘r’ and ‘q’ become bounded
How to find intersection of the parametric curves
- Use of accumulator arrays
- concept of ‘Voting’
- To reduce the computational load use Gradient information
SHT Algorithm
Quantize the Hough Transform space: identify the maximum and minimum values of r and q
Generate an accumulator array A(r, q); set all values to zero
For all edge points (xi, yi) in the image
- Use gradient direction for q
- Compute r from the equation
- Increment A(r, q) by one
For all cells in A(r, q)
- Search for the maximum value of A(r, q)
- Calculate the equation of the line
To reduce the effect of noise more than one element (elements in a neighborhood) in the accumulator array are increased
SHT Algorithm(cont.)
Line equation: y=mx+c presenting in parameter space (c,m)
But this is wrong for vertical lines.
So polar co-ordinates are used as parameter space, i.e. (r,Θ) instead of (c,m).
Advantages of Parameterization
- Values of ‘r’ and ‘q’ become bounded
How to find intersection of the parametric curves
- Use of accumulator arrays
- concept of ‘Voting’
- To reduce the computational load use Gradient information
Quantize the Hough Transform space: identify the maximum and minimum values of r and q
Generate an accumulator array A(r, q); set all values to zero
For all edge points (xi, yi) in the image
- Use gradient direction for q
- Compute r from the equation
- Increment A(r, q) by one
For all cells in A(r, q)
- Search for the maximum value of A(r, q)
- Calculate the equation of the line
To reduce the effect of noise more than one element (elements in a neighborhood) in the accumulator array are increased