Elementary trigonometric quantities are defined in
l
2
,
p
analogously to that in
l
2
,
2
, the sine and cosine functions are generalized for each
p
>
0
as functions
sin
p
and
cos
p
such that they ...satisfy the basic equation
|
cos
p
(
φ
)
|
p
+
|
sin
p
(
φ
)
|
p
=
1
. The
p-generalized radius coordinate of a point
ξ
∈
R
n
is defined for each
p
>
0
as
r
p
=
(
∑
i
=
1
n
|
ξ
i
|
p
)
1
/
p
. On combining these quantities,
l
n
,
p
-spherical coordinates are defined. It is shown that these coordinates are nearly related to
l
n
,
p
-simplicial coordinates. The Jacobians of these generalized coordinate transformations are derived. Applications and interpretations from analysis deal especially with the definition of a generalized surface content on
l
n
,
p
-spheres which is nearly related to a modified co-area formula and an extension of Cavalieri's and Torricelli's indivisibeln method, and with differential equations. Applications from probability theory deal especially with a geometric interpretation of the uniform probability distribution on the
l
n
,
p
-sphere and with the derivation of certain generalized statistical distributions.
An artistic line portrait robot can generate, process, and draw line portraits. Compared to real face images, line portraits lose some recognizable information. Maintaining recognizability during the ...process of expression edition of line portraits is an important challenge for artistic portrait robots. A recognizable expression line portrait synthesis method based on a triangle coordinate system (TCS) is proposed. First, based on public facial expression databases JAFFE, Oulu CASIA, RaFD, and Cohn-Kanade (CK), by studying the feature deviations between different expressions of the same person, an expression deformation constraint criterion (EDCC) that is conducive to maintaining recognizable features is proposed. Then, by comparing features between the source line portrait and reference expression portrait, the expression features are calculated. Finally, under the EDCC, based on expression features, a recognizable expression line portrait is generated through image topological deformation based on TCS. In addition, we can synthesize different degrees of expression line portraits. On the public face datasets (FHHQ, CelebA-HQ, and CK), we implemented qualitative and quantitative contrast experiments. Experimental results demonstrate that this method can automatically synthesize an expression line portrait with reference expression, where the expression degree of the reference expression is controllable, and the generated expression portrait still has high recognizability. The expression samples generated by the proposed method are used for face authentication on the CK dataset, and only 0.22% of the samples fail to pass the authentication.
The separation properties of the aluminium–plastic laminates in postconsumer Tetra Pak structure were studied in this present work. The organic solvent blend of benzene–ethyl alcohol–water was used ...as the separation reagent. Then triangle coordinate figure analysis was taken to optimize the volume proportion of various components in the separating agent and separation process. And the separation temperature of aluminium–plastic laminates was determined by the separation time, efficiency, and total mass loss of products. The results show that cost-efficient separations perform best with low usage of solvents at certain temperatures, for certain times, and within a certain range of volume proportions of the three components in the solvent agent. It is also found that similar solubility parameters of solvents and polyethylene adhesives (range 26.06–34.85) are a key factor for the separation of the aluminium–plastic laminates. Such multisolvent processes based on the combined-system concept will be vital to applications in the recycling industry.
This paper presents a new method based on triangle coordinate system to synthesize multi-feature virtual faces. This method can extract contour features, textural features and facial features among ...faces making use of the mapping relationships of coordinates. We will obtain a number of vectors throughout the processes. By using those vectors users can synthesize virtual faces with different facial features and expressions. The method is visualized, effective and fast.
A novel math method of image morphing Shoujue Wang; Xianyang Liang
2011 3rd International Conference on Computer Research and Development,
2011-March, Letnik:
4
Conference Proceeding
Image morphing has received much attention in recent years. It mainly involves feature specification, geometric transformation and color blending. Here, a novel calculation method of image morphing ...is proposed. First, a novel coordinate system called triangle coordinate system is defined, which has a great advantage in geometric transformation. Second, corresponding feature points on images are marked. Third, cartesian coordinates of all pixels are converted into triangle coordinates for geometric transformation. Finally, color is blended and interpolated. Experiments given in the paper show that the method proposed is practicable.
Multidimensional grey evaluation is an intelligent method for decision evaluation. We distinguish the class of the assessment object according to the maximum of composite weighting coefficients ...vector in grey evaluation. However, we find there are obvious limitations or deficiencies in the practical application. This paper divides three basic types of grey evaluation into ten particular classifications by combining the triangle-coordinate figure with the theory of golden section, which can provide more effective information and reliable scientific evidence for the decision-making. We calculate grey evaluation code by weighted summation of category weights and make the single-level sort. Hence, through the proposed procedure, grey evaluation will be more comprehensive, accurate and credible.
We investigate the method for the determination of an appropriate mixing region of three kinds of antacid, magnesium hydroxide, dried aluminum hydroxide gel and calcium carbonate using trianglular ...coordinates. Using the trianglular coordinates, the appropriate mixing region of satisfying the following categories was determined ; 1) acid neutralizing capacity (200 ml), 2) immediate action (pH 6-8 range obtained 10 min after pouring an antacid into 50 ml of 0.1mol/1 HCl (aq) sol.), 3) bowel property (mol ratio of Mg/Al=1-3), and 4) quantities of combination of three antacids (under 700 mg of total quantities). Modified Fuchs Test was performed at some points which met the above conditions. The durability of the combination of these three antacids was evaluated. The following regions have long durability of antacids (about 60 min for persisting pH 3.5-5); magnesium hydroxide 40-60%, dried aluminum hydroxide gel 30-50% and calcium carbonate 10%. In the cases of changing the above mentioned conditions, and of using different kinds of antacid, the determination of the appropriate mixing region using triangular coordinates is effective for the pharmaceutical technology. In this study we emphasize the following striking features ; utilization of triangular coordinates, fixing the combination of antacid, and incorporation of three kinds of antacid with aluminum, magnesium and calcium.
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