`Name:`

a classifier based on the shape of orientation histograms (SOH) of input images and random forests `Domain:`

Machine learning`Functionality:`

The classifier makes use of SOH feature vectors to classify artcode or non-artcode images`Input:`

$I$: an image to be classified
`Output:`

$Pr$: the probability of being classified as "artcode"
Enhancing Supervised Classifications with Metamorphic Relations https://doi.org/10.1145/3193977.3193978

`Description:`

`Property:`

$\sum_{i=1}^{n}Pr(B_{s_{a}}^{i}) \geq \sum_{i=1}^{n}Pr(B_{s_{n}}^{i})$:
where $n$ is the number of image blocks;
$Pr()$ is the probability to be classified as Artcode by the original classifier;
$B_{s_{a}}^{i}$ denotes the ith block of the Artcode image;
$B_{s_{n}}^{i}$ denotes the ith block of the non-artcode image; `Source input:`

$B_{s_{a}}^{i}$: splitting the input artcode image uniformly into blocks `Source output:`

$Pr(B_{s_{a}}^{i})$: the probability of the blocks being classified as "artcode" `Follow-up input:`

$B_{s_{n}}^{i}$: splitting the input non-artcode image uniformly into blocks
`Follow-up output:`

$Pr(B_{s_{n}}^{i})$: the probability of the blocks being classified as "artcode"
`Input relation:`

$B_{s_{a}}^{i}$: splitting the input artcode image uniformly into blocks, while
$B_{s_{n}}^{i}$: splitting the input non-artcode image uniformly into blocks
`Output relation:`

$\sum_{i=1}^{n}Pr(B_{s_{a}}^{i}) \geq \sum_{i=1}^{n}Pr(B_{s_{n}}^{i})$:
$n$ is the number of image blocks;
$Pr()$ is the probability to be classified as Artcode by the original classifier;
$B_{s_{a}}^{i}$ denotes the ith block of the Artcode image;
$B_{s_{n}}^{i}$ denotes the ith block of the non-artcode image;
`Pattern:`

asymmetry, replacement `Description:`

`Property:`

$\sum_{i=1}^{m}Pr(B_{O_{a}}^{i}) \geq \sum_{i=1}^{m}Pr(B_{O_{n}}^{i})$:
where $m$ is the number of image masks;
$B_{O_{a}}^{i} = \cap(I_{a},M_{i})$ and $B_{O_{n}}^{i} = \cap(I_{n},M_{i})$ outputs the overlapped areas of Artcode and non-Artcode images $Ia$ and $In$ and the ith mask $Mi$;
$Pr()$ is the probability to be classified as Artcode by the original classifier;
$B_{O_{a}}^{i}$ denotes the ith block of the Artcode image;
$B_{O_{n}}^{i}$ denotes the ith block of the non-artcode image;`Source input:`

$B_{O_{a}}^{i}$: splitting the input artcode image (blocks with overlapped areas are permitted) into blocks `Source output:`

$Pr(O_{O_{a}}^{i})$: the probability of the blocks being classified as "artcode" `Follow-up input:`

$B_{O_{n}}^{i}$: splitting the input non-artcode image (blocks with overlapped areas are permitted) into blocks
`Follow-up output:`

$Pr(B_{O_{n}}^{i})$: the probability of the blocks being classified as "artcode"
`Input relation:`

$B_{O_{a}}^{i}$: splitting the input artcode image (blocks with overlapped areas are permitted) into blocks, while
$B_{O_{n}}^{i}$: splitting the input non-artcode image (blocks with overlapped areas are permitted) into blocks
`Output relation:`

$\sum_{i=1}^{m}Pr(B_{O_{a}}^{i}) \geq \sum_{i=1}^{m}Pr(B_{O_{n}}^{i})$:
$m$ is the number of image masks;
$B_{O_{a}}^{i} = \cap(I_{a},M_{i})$ and $B_{O_{n}}^{i} = \cap(I_{n},M_{i})$ outputs the overlapped areas of Artcode and non-Artcode images $Ia$ and $In$ and the ith mask $Mi$;
$Pr()$ is the probability to be classified as Artcode by the original classifier;
$B_{O_{a}}^{i}$ denotes the ith block of the Artcode image;
$B_{O_{n}}^{i}$ denotes the ith block of the non-artcode image;
`Pattern:`

asymmetry, replacement`Description:`

`Property:`

$Pr(B_{O_{a}}^{i}) \geq Pr(B_{S_{a}}^{i})$:
$Pr()$ is the probability to be classified as Artcode by the original classifier;
$B_{O_{a}}^{i}$ denotes the ith block of the artcode image;
$B_{S_{n}}^{i}$ denotes the ith block of the artcode image;`Source input:`

$B_{O_{a}}^{i}$: splitting the input artcode image (blocks with overlapped areas are permitted) into blocks `Source output:`

$Pr(O_{O_{a}}^{i})$: the probability of the blocks being classified as "artcode" `Follow-up input:`

$B_{S_{a}}^{i}$: splitting the input artcode image uniformly into blocks
`Follow-up output:`

$Pr(B_{S_{a}}^{i})$: the probability of the blocks being classified as "artcode"
`Input relation:`

$B_{O_{a}}^{i}$: splitting the input artcode image (blocks with overlapped areas are permitted) into blocks, while
$B_{S_{a}}^{i}$: splitting the input artcode image uniformly into blocks
`Output relation:`

$Pr(B_{O_{a}}^{i}) \geq Pr(B_{S_{a}}^{i})$:
$Pr()$ is the probability to be classified as Artcode by the original classifier;
$B_{O_{a}}^{i}$ denotes the ith block of the artcode image;
$B_{S_{n}}^{i}$ denotes the ith block of the artcode image;
`Pattern:`

asymmetry, replacement