From 3D Point Clouds to Pose-Normalised Depth Maps

We consider the problem of generating either pairwise-aligned or pose-normalised depth maps from noisy 3D point clouds in a relatively unrestricted poses. Our system is deployed in a 3D face alignment application and consists of the following four stages: (i) data filtering, (ii) nose tip identification and sub-vertex localisation, (iii) computation of the (relative) face orientation, (iv) generation of either a pose aligned or a pose normalised depth map. We generate an implicit radial basis function (RBF) model of the facial surface and this is employed within all four stages of the process. For example, in stage (ii), construction of novel invariant features is based on sampling this RBF over a set of concentric spheres to give a spherically-sampled RBF (SSR) shape histogram. In stage (iii), a second novel descriptor, called an isoradius contour curvature signal, is defined, which allows rotational alignment to be determined using a simple process of 1D correlation. We test our system on both the University of York (UoY) 3D face dataset and the Face Recognition Grand Challenge (FRGC) 3D data. For the more challenging UoY data, our SSR descriptors significantly outperform three variants of spin images, successfully identifying nose vertices at a rate of 99.6%. Nose localisation performance on the higher quality FRGC data, which has only small pose variations, is 99.9%. Our best system successfully normalises the pose of 3D faces at rates of 99.1% (UoY data) and 99.6% (FRGC data)

The Keyes to Reclaiming the Racial History of the Roberts Court

This article advocates for a fundamental re-understanding about the way that the history of race is understood by the current Supreme Court. Represented by the racial rights opinions of Justice John Roberts that celebrate racial progress, the Supreme Court has equivocated and rendered obsolete the historical experiences of people of color in the United States. This jurisprudence has in turn reified the notion of color-blindness, consigning racial discrimination to a distant and discredited past that has little bearing to how race and inequality is experienced today. The racial history of the Roberts Court is centrally informed by the context and circumstances surrounding Brown v. Board of Education. For the Court, Brown symbolizes all that is wrong with the history of race in the United States - legal segregation, explicit racial discord, and vicious and random acts of violence. Though Roberts Court opinions suggest that some of those vestiges still exits, the bulk of its jurisprudence indicate the opposite. With Brown’s basic factual premises as its point of reference, the Court has consistently argued that the nation has made tremendous strides away from the condition of racial bigotry, intolerance, and inequity. The article accordingly argues that the Roberts Court reliance on Brown to understand racial progress is anachronistic. Especially as the nation’s focus for racial inequality turned national in scope, the same binaries in Brown that had long served to explain the history of race relations in the United States (such as Black-White, North-South, and Urban-Rural) were giving way to massive multicultural demographic and geographic transformations in the United States in the years and decades after World War II. All of the familiar tropes so clear in Brown and its progeny could no longer fully describe the current reality of shifting and transforming patterns of race relations in the United States. In order to reclaim the history of race from the Roberts Court, the article assesses a case that more accurately symbolizes the recent history and current status of race relations today: Keyes v. School District No. 1. This was the first Supreme Court case to confront how the binaries of cases like Brown proved of little probative value in addressing how and in what ways race and racial discrimination was changing in the United States. Thus, understanding Keyesand the history it reflects reveals much about how and in what ways the Roberts Court should rethink its conclusions regarding the history of race relations in the United States for the last 60 years

The Keyes to Reclaiming the Racial History of the Roberts Court

This article advocates for a fundamental re-understanding about the way that the history of race is understood by the current Supreme Court. Represented by the racial rights opinions of Justice John Roberts that celebrate racial progress, the Supreme Court has equivocated and rendered obsolete the historical experiences of people of color in the United States. This jurisprudence has in turn reified the notion of color-blindness, consigning racial discrimination to a distant and discredited past that has little bearing to how race and inequality is experienced today. The racial history of the Roberts Court is centrally informed by the context and circumstances surrounding Brown v. Board of Education. For the Court, Brown symbolizes all that is wrong with the history of race in the United States - legal segregation, explicit racial discord, and vicious and random acts of violence. Though Roberts Court opinions suggest that some of those vestiges still exits, the bulk of its jurisprudence indicate the opposite. With Brown’s basic factual premises as its point of reference, the Court has consistently argued that the nation has made tremendous strides away from the condition of racial bigotry, intolerance, and inequity. The article accordingly argues that the Roberts Court reliance on Brown to understand racial progress is anachronistic. Especially as the nation’s focus for racial inequality turned national in scope, the same binaries in Brown that had long served to explain the history of race relations in the United States (such as Black-White, North-South, and Urban-Rural) were giving way to massive multicultural demographic and geographic transformations in the United States in the years and decades after World War II. All of the familiar tropes so clear in Brown and its progeny could no longer fully describe the current reality of shifting and transforming patterns of race relations in the United States. In order to reclaim the history of race from the Roberts Court, the article assesses a case that more accurately symbolizes the recent history and current status of race relations today: Keyes v. School District No. 1. This was the first Supreme Court case to confront how the binaries of cases like Brown proved of little probative value in addressing how and in what ways race and racial discrimination was changing in the United States. Thus, understanding Keyesand the history it reflects reveals much about how and in what ways the Roberts Court should rethink its conclusions regarding the history of race relations in the United States for the last 60 years

Of Greater Value than the Gold of Our Mountains : The Right to Education in Colorado\u27s Nineteenth- Century Constitution

As the contemporary battle for educational opportunity has moved to state courts, the education clauses of a state\u27s constitution have played prominent roles in the litigation. Of particular concern has been the role that history should play in interpreting the scope and meaning of various provisions of a clause. This Article advances this debate by examining the development of article IX (the education clause) in Colorado\u27s 1876 Centennial Constitution. The Article first details the efforts to provide free public education in the United States in the decades leading to the drafting of the Colorado state constitution in 1876. Colorado, as part of a nationwide movement to ensure public education as a state constitutional right, reflected a much larger conversation over the scope and meaning of education to citizenship and civic engagement, economic opportunity, public versus private right, and, in some cases, civil rights. The Article accordingly turns to how these issues emerged quite pointedly in Colorado: from the discovery of gold on the banks of the Platte River and the opening of the first schoolhouse in 1859, to its formation as a territory and the subsequent passage of a comprehensive School Law in 1861, to internal and external debates over the education clause that eventually came to be drafted and adopted by the Framers to the state\u27s constitution. While Colorado\u27s pioneers struggled to reconcile competing visions over the precise role that a statewide system of education should play, they nevertheless were in agreement that it be thorough and uniform for all of the state\u27s students now and into the future. As the final part of the Article documents, however, it was readily apparent that systemic and structural inequities were already dividing the state\u27s emerging school districts in the immediate years after statehood. Part of a much larger nineteenth-century commitment to public education, Colorado\u27s early legal experiences reflected the hopes, aspirations, and maddening limits of a substantive and meaningful constitutional right to education that would be available for all of its habitants

The Keyes to Reclaiming the Racial History of the Roberts Court

This Article advocates for a fundamental re-understanding about the way that the history of race is understood by the current Supreme Court. Represented by the racial rights opinions of Justice John Roberts that celebrate racial progress, the Supreme Court has equivocated and rendered obsolete the historical experiences of people of color in the United States. This jurisprudence has in turn reified the notion of color-blindness, consigning racial discrimination to a distant and discredited past that has little bearing to how race and inequality is experienced today. The racial history of the Roberts Court is centrally informed by the context and circumstances surrounding Brown v. Board of Education. For the Court, Brown symbolizes all that is wrong with the history of race in the United States— legal segregation, explicit racial discord, and vicious and random acts of violence. Though Roberts Court opinions suggest that some of those vestiges still exits, the bulk of its jurisprudence indicate the opposite. With Brown’s basic factual premises as its point of reference, the Court has consistently argued that the nation has made tremendous strides away from the condition of racial bigotry, intolerance, and inequity. The Article accordingly argues that the Roberts Court reliance on Brown to understand racial progress is anachronistic. Especially as the nation’s focus for racial inequality turned national in scope, the same binaries in Brown that had long served to explain the history of race relations in the United States (such as Black- White, North-South, and Urban-Rural) were giving way to massive multicultural demographic and geographic transformations in the United States in the years and decades after World War II. All of the familiar tropes so clear in Brown and its progeny could no longer accurately describe the current reality of shifting and transforming patterns of race relations in the United States. In order to reclaim the history of race from the Roberts Court, the Article assesses a case that more accurately symbolizes the recent history and current status of race relations today: Keyes v. School District No. 1. This was the first Supreme Court case to confront how the binaries of cases like Brown proved of little probative value in addressing how and in what ways race and racial discrimination was changing in the United States. Thus, understanding Keyes and the history it reflects reveals much about how and in what ways the Roberts Court should rethink its conclusions regarding the history of race relations in the United States for the last 60 years